CTR
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{n^2}\) <1 (n thuộc Z, n>= 2)
Lời giải:
Ta có: \(n^2=n.n> (n-1)n\) với mọi \(n\geq 2\)
\(\Rightarrow \frac{1}{n^2}< \frac{1}{n(n-1)}\)
Do đó:
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< \underbrace{\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{n(n-1)}}_{N}(1)\)
Lại có: \(N=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{n-(n-1)}{(n-1)n}\)
\(N=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n-1}-\frac{1}{n}=1-\frac{1}{n}< 1(2)\)
Từ (1); (2) theo nguyên tắc bắc cầu suy ra:
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{n^2}< 1\)
Ta có đpcm.
tìm số tự nhiên n biết
a) 5⋮(n+1)
b) (n+4)⋮(n+1)
c) (3.n +15)⋮(n+2)
Cho A= 1/2+1/2^2+1/2^3+1/2^4+-..+1/2^10
Chứng tỏ rằng A + 1/2^10 = 1
giúp mình nhé các bạn
thực hiện hép tính sau
\(\dfrac{3}{8}+\dfrac{5}{8}\)
\(\dfrac{-1}{2}+\dfrac{5}{7}\)
\(\dfrac{9}{11}.\dfrac{5}{8}\)
\(\dfrac{3}{4}:\dfrac{4}{3}\)
đổi phân số \(\dfrac{7}{3}\)ra hỗn số
viết hỗn số \(4\dfrac{3}{7}\)
tính \(1\dfrac{3}{4}+3\dfrac{5}{9}\)
tính \(1\dfrac{5}{4}-2\dfrac{7}{4}\)
xét bài toán sau : \(\dfrac{3}{5}\)số học sinh lớp 6a là 27 bạn. Hỏi lớp 6a có bao nhiêu học sinh ?
BT4
a) vẽ tam giác ABC biết độ dài các cạnh là : AB = 3cm ; BC= 4cm; AC= 5cm
b) đo góc B của tam giác ABC
giúp mình đi
Ba lớp 6A, 6B, 6C phải trồng một số cây quanh trường nhân ngày kỉ niệm sinh nhật Bác 19https:https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.LogaVN.nethttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.imagehttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.faqhttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.data2https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.775362_.5. Lớp 6A trồng được 1https:https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.LogaVN.nethttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.imagehttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.faqhttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.data2https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.775362_.4 số cây , lớp 6B trồng được 2https:https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.LogaVN.nethttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.imagehttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.faqhttps:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.data2https:https://LogaVN.net/image/faq/data2/710107_.https://LogaVN.net/image/faq/data2/710107_.LogaVN.nethttps://LogaVN.net/image/faq/data2/710107_.imagehttps://LogaVN.net/image/faq/data2/710107_.faqhttps://LogaVN.net/image/faq/data2/710107_.data2https://LogaVN.net/image/faq/data2/710107_.185200_.775362_.5 tổng số cây, lớp 6C trồng nốt 105 cây còn lại.
a. Tính tổng số cây
b.Tính số cây trông được của lớp 6A và tỷ số phần trăm số cây trồng được lớp 6 với tổng số cây
HELP ME
Khẳng định nào trong các khẳng định sau là đúng?
A.Góc 600 và góc 300 là hai góc kề nhau.
B.Góc bẹt là góc có hai cạnh là hai tia đối nhau.
C.Nếu xOz + xOy = zOy thì Ox là tia phân giác của zOy.
D.Nếu OA nằm giữa hai tia OB và OC thì AOB + BOC = AOC.
(Lưu ý:Đọc kĩ nha bài này dễ nhầm lắm đó ^-^
Vì mk ko bik viết dấu mũ của góc nên -- các bạn tự hiểu nhé)
1,Thực hiện phép tính:
1 - 2 + 3 - 4 + 5 - 6 + --..+2011 - 2012
\(\dfrac{7}{9}\) - \(\dfrac{\left|X\right|}{3}\) = \(\dfrac{1}{9}\)
Cho \(A=\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{2014\cdot2015\cdot2016}\).
Chứng minh \(A\le\dfrac{1}{4}\).
giúp mk vs !!!
A=1-2+3-4+5-6+-..+2011-2012
Tính giá trị ha^^^
Ai xong tc mk để avatar 1 tuần nha)!!!
Cho góc xOy = 120 độ và điểm A trong góc xOysao cho góc yOA = 75 độ và điểm B không nằm trong góc xOy sao cho góc xOB = 135 độ . Chứng tỏ rng ba điểm A , O , B thẳng hàng .
Giúp mình với nha ! Mình cảm ơn nhiều !
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