I'm stuck on this....

Problem:

Show that (tn) is a nonincreasing sequence. That is, use induction to prove that $\displaystyle t_{n} \geq t_{n+1}$ where $\displaystyle t_{n+1}=\left(1-\frac{1}{(n+1)^2}\right)t_{n}.$

I have the base case so, $\displaystyle 1 \geq \frac{3}{4}$. Then assume $\displaystyle t_{k} \geq t_{k+1}$.

But I'm stuck at this part. I don't know how to arrive at $\displaystyle t_{k+1} \geq t_{k+2}$. I tried messing with the inequalities and stuff, but I'm still not sure.

Edit: The only thing I could really come up with was .....

$\displaystyle (1-\frac{1}{(k+1)^2}) \geq (1-\frac{1}{(k+1)^2})(1-\frac{1}{(k+2)^2}$ then use the fact $\displaystyle t_{k+1}=1-\frac{1}{(k+1)^2}$ and so $\displaystyle \frac{t_{k+1}}{t_{k}}=1-\frac{1}{(n+1)^2}.$