for a series to be decreasing the next term must be smaller than the current term. $\displaystyle a_n > a_{n +1}$show $\displaystyle \{ \frac{1}{2n + 1} \}_{n = 1}^{\infty}$ is strictly decreasing.

2n +1 < 2(n +1) + 1 (n^th term and n^th + 1)

2n + 1 < 2n +3

$\displaystyle \frac{1}{2n +1} > \frac{1}{2n + 3}$

the next term is less than the previous therfor the series is decreasing.

Am I correct?