Let be a real number and consider the series whose th term is for

MATHEMATICS · Subjective · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

Let

p

be a real number and consider the series whose

n

th term is

a_n(p) = (n+1)^p - n^p

for

n \ge 1

. Determine all values of

p

for which the series converges.