Question

[Funky]

Cho s=1+2+2²+2³+...+2⁹⁹ so sánh S với 2¹⁰⁰

Answer 1

[Akai Haruma]

Lời giải:

$S=1+2+2^2+2^3+2^4....+2^{99}$

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

Trừ theo vế ta có:

$2S-S=(2+2^2+2^3+...+2^{100})-(1+2+2^3+..+2^{99})=2^{100}-1$

$S=2^{100}-1< 2^{100}$