Question

Tính các tổng sau:

a) A=\(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{100}}\)

b) B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{102^2}\)

c) C=\(\dfrac{3}{1+2}+\dfrac{3}{1+2+3}+\dfrac{3}{1+2+3+4}+...+\dfrac{3}{1+2+3+...+100}\)

Answer 1

a) \(A=\dfrac{1}{2}+\dfrac{1}{2^2}+............+\dfrac{1}{2^{100}}\)

\(\Leftrightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+........+\dfrac{1}{2^{99}}\)

\(\Leftrightarrow2A-A=\left(1+\dfrac{1}{2}+.........+\dfrac{1}{2^{99}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+.....+\dfrac{1}{2^{100}}\right)\)

\(\Leftrightarrow A=1-\dfrac{1}{2^{100}}\)

Answer 2

Nguyễn Thanh Hằng Tiếp đi Hằng

Answer 3

Mặc dù t cx k biết làm nhưng mà trẩu qá Hằng