47. Tính nhanh.

a) ; b) .

Tìm x biết:

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+-..+\dfrac{2}{x.\left(x+1\right)}\)

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Bài 1: So sánh

a) A=\(\dfrac{13^{15}+1}{13^{16}+1}\) và B=\(\dfrac{13^{16}+1}{13^{17}+1}\)

b) C=\(\dfrac{1999^{1999}+1}{1999^{2000}+1}\) và D=\(\dfrac{1999^{1998}+1}{1999^{1999}+1}\)

Bài 2: So sánh các ps sau một cách hợp lý

a) \(\dfrac{29}{33};\dfrac{22}{37};\dfrac{29}{37}\)

b) \(\dfrac{163}{257};\dfrac{163}{221};\dfrac{149}{257}\)

Thực hiện phép tính

a) \(\dfrac{1}{2}.\left(\dfrac{2}{9}+\dfrac{3}{7}-\dfrac{5}{27}\right)\) b) \(\left(\dfrac{-5}{28}+1,75+\dfrac{8}{35}\right):\left(-3\dfrac{9}{20}\right)\)

c) \(\dfrac{1}{3}.\dfrac{5}{7}-\dfrac{7}{27}.\dfrac{36}{14}\) d) \(70,5-528:\dfrac{15}{2}\)

Tìm x biết :

7 + 2x+1 = 28 - [ 42 - ( 22 -1 )]

Tìm số tự nhiên abc biết 1000/a+b+c=abc.

a) Cho A=1-7+13-19+25-31+... Biết A có 20 số hạng. Tính giá trị của A

b) Tìm hai số tự nhiên a và b, biết a>b; a+b=16 và ƯCLN(a,b) =4

a) Cho a;b;c \(\in\)Z biết ab - ac + bc - c2 = -1. Chứng tỏ a và b là hai số đối nhau.

b) Cho a;b;c;d \(\in\)Z biết a.b là số liền sau của c.d và a + b = c + d, Chúng tỏ a = b

Tuổi cha hiện nay bằng \(\dfrac{11}{4}\) tuổi con hiện nay. Sau 4 năm nữa, tuổi cha sẽ gấp 3 lần tuổi con hiện nay. Tính tuổi của mỗi người.