# calculation – Show that the series is convergent and less than 1

Show that the series

$$sum_ {k = 1} ^ { infty} dfrac {2} {(k + 1) (2k + 1)}$$

is convergent and converges to a number less than $$1$$.

I tried the quotient test for the series, but it did not work. I do not know what else to do. Any index would be very appreciated.
Thank you!