Question

s =1+2+2²+2³......+2⁹⁹+2¹⁰⁰=?​

Answer 1

Răspuns:

Explicație pas cu pas:

s = 1 + 2 + 2^2 + 2^3 + ... + 2^99 + 2^100

2s = 2 + 2^2 + 2^3 + 2^4 + ... + 2^100 + 2^101

2s - s = 2 + 2^2 + 2^3 + 2^4 + ... + 2^100 + 2^101 - (1 + 2 + 2^2 + 2^3 + ... + 2^99 + 2^100)

s = 2 + 2^2 + 2^3 + 2^4 + ... + 2^100 + 2^101 - 1 - 2 - 2^2 - 2^3 - ... - 2^99 - 2^100 = 2^101 - 1