Question

[Đinh Văn Vượng]

1. 1 + 1/4 + 1/8 + 1/16 + 1/32 + ........+ 1/512

Answer 1

[Akai Haruma]

Lời giải:
Gọi tổng trên là A

$A=1+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{512}$

$2\times A=2+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}$

$2\times A-A=(2+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256})-(1+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+...+\frac{1}{512})$

$A=2+\frac{1}{2}-(1+\frac{1}{512})$

$A=\frac{767}{512}$