How can I raise my intuition in solving mathematical problem?
Solution 1:
I don't know. Was it my ‘feminine intuition’ that helped me realize that $\displaystyle\sum_{n=0}^\infty\left[\frac{(2n-3)!!}{(2n)!!}\right]^2=\frac4\pi$, or merely plucking $n=\frac12$ into Vandermonde's formula $\displaystyle\sum_{k=0}^n{n\choose k}^2={2n\choose n}$, and using the fact that $\Gamma\left(\frac12\right)=\sqrt\pi$ ? :-)