MathDB

1980 VTRMC #2

Source:

August 11, 2020

Problem Statement

The sum of the first

n

terms of the sequence

1,1+2,1+2+2^2,\ldots,1+2+\cdots+2^{k-1},\ldots

is of the form

2^{n+R}+Sn^2+Tn+U

for all

n>0.

Find

R,S,T,

and

U.