Question

Chứng minh rằng:

A=1+3^2+3^4+...+3^50

a)A=3^52-1/8

b)8A+1=81^13

Answer 1

Lời giải:

a.

$A=1+3^2+3^4+....+3^{50}$

$3^2A=3^2+3^4+3^6+....+3^{52}$

$\Rightarrow 3^2A-A=(3^2+3^4+3^6+....+3^{52}) - (1+3^2+3^4+....+3^{50})$

$\Rightarrow 8A=3^{52}-1$
$\Rightarrow A=\frac{3^{52}-1}{8}$ (đpcm)

b.

Có: $8A=3^{52}-1=(3^4)^{13}-1=81^{13}-1$

$\Rightarrow 8A+1=81^{13}$ (đpcm)