Question

s=1-5+52-53+...+598-5⁹⁹
a) tính S
b) CMR : 5100chia cho 6 dư 1

Answer 1

Lời giải:
$S=1-5+5^2-5^3+...+5^{98}-5^{99}$

$5S=5-5^2+5^3-5^4+....+5^{99}-5^{100}$

$5S+S=(1-5+5^2-5^3+...+5^{98}-5^{99})+(5-5^2+5^3-5^4+....+5^{99}-5^{100})$

$6S=-5^{100}+1$

$S=\frac{1-5^{100}}{6}$

b.

$1-5^{100}=6S$

$5^{100}=1-6S\Rightarrow 5^{100}$ chia $6$ dư $1$.