# How would you solve it: Part 4

**Calculus**Level 5

\[ \large \displaystyle \sum_{n=0}^{\infty}\dfrac{(-1)^{n}}{n+1}{2n \choose n}^{-1} = \dfrac{\alpha}{\sqrt{\beta}}\ln^{\eta}{\phi} - \delta(\ln^{\gamma}{\phi}) \]
If the above summation is true for positive integers: \( \alpha,\beta,\gamma,\delta,\eta \) and that
\(\beta\) is a prime, then compute:
\[ \alpha+\beta+\gamma+\delta+\eta\].

Note that: \(\phi\) is the Golden ratio

This is \(95\) % Original