let a_i = 2^i
20
Find Σ a_(i+1)-a_i
i=1
Note the sum. You have
a2-a1 + a3-a2 + a4-a3 + ... + a21-a20
= a21-a1
= 2^21 - 2^1
There's really no reason to write the sum as you did. Since you know a_i explicitly, it would be better just to say
20
Σ 2^(i+1)-2^i
i=1