Question

Tính nhanh 

a) 1 + 2^3 + 2^6 + 2^9 + ..... + 2^99

b) 1 + 2 + 2^2 + 2^3 + .... + 2^100

Answer 1

1.

$A=1+2^3+2^6+2^9+...+2^{99}$

$2^3A=2^3+2^6+2^9+2^{12}+...+2^{102}$

$\Rightarrow 2^3A-A=2^{102}-1$

$\Rightarrow 7A=2^{102}-1$
$\Rightarrow A=\frac{2^{102}-1}{7}$

Answer 2

2.

$B=1+2+2^2+2^3+...+2^{100}$

$2B=2+2^2+2^3+2^4+...+2^{101}$

$\Rightarrow 2B-B=2^{101}-1$

$\Rightarrow B=2^{101}-1$