Using induction, show that ∀n∈N \ {0,1}, 1 + 1/(2^2) + … + 1/(n^2) > 3n/(2n + 1)

Question

∀n∈N \ {0,1}, 1 + 1/(2^2) + … + 1/(n^2) > 3n/(2n + 1)

N denotes the Natural Numbers. I tried adding 1/(n+1)^2 to both sides but am stuck.

Answer 1

If you get to that point, now you have to show that

3n/(2n + 1)+1/(n+1)^2>=(3(n+1))/(2(n+1))=(3n+3)/(2n+3).

I think you manage that.