Let , and . As becomes very large, which sum grows the…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

S_1(n)=\sum_{k=1}^{n} k

S_2(n)=\sum_{k=1}^{n} k^{2}

and

S_3(n)=\sum_{k=1}^{n} k^{3}

. As

n

becomes very large, which sum grows the fastest? (a)

S_2(n)

(b)

S_3(n)

S_1(n)