# Math Help - limit

1. ## limit

Hi,

need some help with this problem

a. Show that, whatever is the whole number, k is superior or equal to 2;

1/k^2 is less than or equal to 1/ k-1 - 1/ K

Have done this and think I have the answer but part 2 and 3 are complicated

b. Use this result to show the inequality

n 1
€ ----- is less than or equal to
k=2 K^2

n
c. Show that (Un) which is defined by Un=€ .1...
k=2 K^2 is convergent

Thanks in advance for any hints to proceed...

2. $\begin{gathered}
\left( {\forall n \geqslant 2} \right)\left[ {\frac{1}
{{n^2 }} \leqslant \frac{1}
{{n - 1}} - \frac{1}
{n}} \right] \hfill \\
\sum\limits_{n = 2}^K {\frac{1}
{{n^2 }}} \leqslant n = \sum\limits_{n = 2}^K {\left[ {\frac{1}
{{n - 1}} - \frac{1}
{n}} \right]} = 1 - \frac{1}
{K} \hfill \\
\end{gathered}$