Find the n th term and the sum to n terms of the series: 1+(1+2)+(1+2+2^2)+...
1+2^1+2^2+...+2^n = 2^(n+1)-1
So, the sequence becomes
2^1-1 + 2^2-1 + 2^3-1 + ... + 2^n-1
= 2^1 + 2^2 + ... + 2^n - n
= 2^(n+1)-1 - n-1
= 2^(n+1) - (n+2)
check (n=5):
1+3+7+15+31 = 2^6-7 = 57