For the sequence with positive integer

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For the sequence

S_n=\displaystyle \int_0^{\pi/2} \sin^{n}x\,dx

with positive integer

n

, state whether

S_{n+1}

is greater than, equal to, or less than

S_n

and briefly justify your answer.