What is the sum of these infinite series in statistics?

[freedominator]

My statistics professor wanted me to remember an infinite series sum, but i can't remember what it was
i think it was either ( E(1/n^2) 1 to infinite ) or ( E(1/(L+n^2)) 0 to infinite ) or ( E(a^n) 0 to infinite where n is between 0 and 1)
i think it was the 2nd one, does anyone know how to calculate either of these?

 

[mfb]

E should be the sum symbol($\Sigma$)?
The first one has a simple solution, I don't think I ever saw any closed form for the second.
At the third one, do you mean "a is between 0 and 1"? In that case, it has a nice value as well, which is very useful to know.