Question

Tính tổng:

S=3+\(\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\)

Answer 1

Giải:

\(S=3.\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)\)

\(2S=3.\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)\)

\(2S-S=3.\left[\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)\right]\)

\(S=3.\left(2-\dfrac{1}{2^9}\right)\)

\(S=3.\dfrac{1023}{512}\)

\(S=\dfrac{3069}{512}\)

Answer 2

2.S= \(6\) + \(3\) + \(\dfrac{3}{2}\) + ..... + \(\dfrac{3}{2^8}\)

2.S - S= ( \(6\) + \(3\) + \(\dfrac{3}{2}\) + ..... + \(\dfrac{3}{2^8}\)) - (\(3\) + \(\dfrac{3}{2}\) + \(\dfrac{3}{2^2}\) + ..... + \(\dfrac{3}{2^9}\))

S= 6 - \(\dfrac{3}{2^9}\)

S= \(\dfrac{6.512}{512}\) - \(\dfrac{3}{512}\) = \(\dfrac{3069}{512}\)

Bn tự rút gọn nha, mk hơi nhát