1+2*2+3*2^2+4*2^3+...+50*2^49=?

Question

1+2*2+3*2^2+4*2^3+...+50*2^49=?

Answer 1

1 = 1•1^0
2•2 = 2•2^1
S = [(1+50•2^49)/2)•50] = (1 + 50•2^49)•25 =
= 25 + 25•2^50 = 25•(1+2^50) =
Известно, что 2^10 = 1024
1024^5 = примерно 10^18
= примерно 25•10^18