Showing that two infinite series converge to the same value

Question

I was preparing for my exam and came across this problem.

Show that

The series on the left hand side is the power series of $\ln(1+x)$ evaluated at $x=1$. This is what i've done so far.

From this point on wards i do not know how to approach this problem since the required infinite series is at $t=1$. Any insight or answers are greatly appreciated ! Thanks

Answer 1

$$\frac{1}{2n(2n-1)}=\frac{1}{2n-1}-\frac1{2n}$$