## ration of $M/N$ in $2$ alternating series

If $$M= \displaystyle \frac{1}{90\cdot 46}+\frac{1}{89\cdot 47}+\cdots \cdots \cdots ++\frac{1}{46\cdot 90}$$

and $$\displaystyle N = 1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots \cdots -\frac{1}{90}.$$ Then $$M/N$$ is

Plan $$N=\bigg(1+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{90}\bigg)-2\bigg(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\cdots \bigg)$$

How do i convert $$M$$ into $$N$$ form . Help me please