1962 AHSME Problems/Problem 32
Problem
If for
and
, find
.
Solution
The sequence is an arithmetic sequence since every term is
more than the previous term. Letting
and
, we can rewrite the sequence as
.
Recall that the sum of the first
terms of an arithmetic sequence is
.
Substituting our values for
and
, we get $n+\frac{\binom{n}2}2}$ (Error compiling LaTeX. Unknown error_msg). Simplifying gives