# Prove by induction that for every n ≥ 1 we have?

##### 1 Answer

Jul 30, 2018

=

Which checks with the series for term (n+1)

#### Explanation:

Let

First we must check that it fits for n=1:

Left side:

Right side:

**So if it is correct for #S_n#, we want to show that
#S_(n+1) = (n+1)/[2(n+1)+1)#**

We have:

=

=

=

=

As this is the same as the right side of our series for term (n+1), the expression checks.