Question

Evaluate the following infinite series\[\sum_{n=1}^{\infty}{\frac{1}{n^2}}\]

Answer 1

Hard stuff huh?

Answer 2

not really, just trying to remember which thing to use... you're gonna end up with something like pi^2/constant

Answer 3

pi^2/6. There a lots of ways to show this ...

Answer 4

What's the easiest way to show it? My CAS says it is \[\frac{\pi ^2}{6}\]

Answer 5

therefore , its value is approximately 1