Cho B=5/5.8.11+5/8.11.14+...+5/302.305.308
Chứng minh B<1/48
Lời giải:
\(B=\frac{5}{5.8.11}+\frac{5}{8.11.14}+...+\frac{5}{302.205.308}\)
\(\Rightarrow \frac{6}{5}B=\frac{6}{5.8.11}+\frac{6}{8.11.14}+...+\frac{6}{302.305.308}\)
\(=\frac{11-5}{5.8.11}+\frac{14-8}{8.11.14}+...+\frac{308-302}{302.305.308}\)
\(=\frac{1}{5.8}-\frac{1}{8.11}+\frac{1}{8.11}-\frac{1}{11.14}+...+\frac{1}{302.305}-\frac{1}{305.308}\)
\(=\frac{1}{5.8}-\frac{1}{305.308}< \frac{1}{5.8}\)
\(\Rightarrow B< \frac{1}{40}.\frac{5}{6}\Leftrightarrow B< \frac{1}{48}\)
Tinh nhanh neu co the:
\(2-\dfrac{2}{3+\dfrac{1}{2}}\)
\(\dfrac{1-\dfrac{1}{\dfrac{3}{4}+1}}{3}\)
chứng minh A=1+1/2+1/3+...+1/100 không phải số tự nhiên .
HELP ME !!!!!AI LÀM ĐÚNG MÌNH TICK CHO NHA !
Bài 1
Cho phân số a/b khác 1 . Tìm phân số c/d sao cho a/b + c/d = a/b . c/d
aaa:a
abab: ab
abc abc:abc
X-40%=36
tính
\(G=\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)...\left(1-1\dfrac{2}{7}\right)\left(1-1\dfrac{3}{7}\right)\)
1. E = \(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+\dfrac{3}{13.16}+\dfrac{3}{16.19}+\dfrac{3}{19.22}\)
2. (x-4)(x-5)=0
30%x+x=52
Tìm x biết :
\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{\left(2x-2\right)2x}=\dfrac{1}{8}\left(x\in N,x\ge2\right)\)
Chứng minh
\(\dfrac{1}{2}\) + \(\dfrac{1}{2^2}\) + ... + \(\dfrac{1}{2^{30}}\) < 1
Loga.vn - Cộng Đồng Luyện Thi Trực Tuyến