$(15$ points$)$ Write a recursive method to compute the following series:

$()=$

$1$

$3$

$+$

$2$

$5$

$+$

$3$

$7$

$+$

$4$

$9$

$+$

$5$

$11+$

$6$

$13++$

$$

$2+1$

Write a test program that displays $()$ for $=1,2,3,,10.$