Question

c) 1 + 2^2 + 2 ^3+ 2^4 + ...+ 2^2015 ^=la puterea​

Answer 1

Răspuns:

Explicație pas cu pas:

S =  1 + 2^2 + 2 ^3+ 2^4 + ...+ 2^2015

2S =  2 + 2^3+ 2^4 + 2^5 +...+ 2^2016

2S - S = 2 + 2 ^3+ 2^4 + ...+ 2^2016 - 1 - 2^2 - 2^3 - 2^4 - 2^5- ....- 2^2015

S = 2 + 2^2016 - 1 - 2^2 = 2^2016 + 2 - 1 - 4 = 2^2016 - 3