What do the sum of the reciprocal of n squared make if n is a natural number?

Question

I’ve recently found out that $\sum_{n=1}^{\infty}\frac{1}{n^2+n}$ makes 1, since it becomes $\frac{1}{2}, \frac{2}{3}$ and so on. After then, I’ve became curious if I do the same thing with the reciprocal of n squared, or $$\sum_{n=1}^{\infty} \frac{1}{n^2}$$ I couldn’t find out the answer. Their sums don’t make a neat form like $\frac{a}{a+1}$. Could anyone tell me what it approaches to?

Answer 1

The sum is $\pi^2/6$. Euler first figured that out. It's no surprise and no disgrace that you didn't. See https://en.wikipedia.org/wiki/Basel_problem .