Câu hỏi của Nguyễn Thùy Nhung

Question

Tính tổng đại số sau:

s=1-2+2²-2³+...+2¹⁰⁰

o0o I am a studious person o0o · Accepted Answer

$S=1-2+2^2-2^3+.....+2^{100}$

$\Rightarrow2S=2-2^2+2^3-......-2^{101}$

$\Rightarrow3S=2S+S=\left(2-2^2+2^3-....-2^{101}\right)+1-2+2^2-2^3+....+2^{100}$

$\Rightarrow3S=-2^{101}+1$

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

Câu trả lời:

$S=1-2+2^2-2^3+.....+2^{100}$

$\Rightarrow2S=2-2^2+2^3-......-2^{101}$

$\Rightarrow3S=2S+S=\left(2-2^2+2^3-....-2^{101}\right)+1-2+2^2-2^3+....+2^{100}$

$\Rightarrow3S=-2^{101}+1$

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