Câu hỏi của NGUYEN DIEU LINH

Question

S6 = 1 + 1/2 + 1/2²+ 1/2³ + ......+1/2¹⁰⁰

^{Tính S}

Le Thi Khanh Huyen · Accepted Answer

$\frac{S.6}{2}=3S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{101}}$

$\Rightarrow6S-3S=3S=1-\frac{1}{2^{201}}=\frac{2^{101}-1}{2^{101}}$

$\Rightarrow S=\frac{2^{101}-1}{3.2^{101}}$

Câu trả lời:

$\frac{S.6}{2}=3S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{101}}$

$\Rightarrow6S-3S=3S=1-\frac{1}{2^{201}}=\frac{2^{101}-1}{2^{101}}$

$\Rightarrow S=\frac{2^{101}-1}{3.2^{101}}$