Question

1 +2+2la a 2+...+2la 100

Answer 1

1+2+2^2+...+2^100=2^101 -1

Am aplicat: 1+2+2^2+...+2^n=2^(n+1) -1

OK!

Fie A=1+2+2^2+...+2^100

2A=2(1+2+2^2+...+2^100)

2A=2+2^2+2^3+...+2^100+2^101, adunam si scadem ''1''.

2A=(1+2+2^2+...+2^100)+2^101 -1

2A=A+2^101 -1

A=2^101 -1

1+2+2^2+...+2^100=2^101 -1