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**wintersoltice** 1.Prove by induction that $\displaystyle \sum_{r=1}^{n}(\frac{1}{r(r+1)(r+2)}) $$\displaystyle =$$\displaystyle \frac{n(n+3)}{4(n+1)(n+2)}$.

Show that $\displaystyle \frac{n(n+3)}{4(n+1)(n+2)}$ is LESSER than $\displaystyle \frac{1}{4}$ for all positive integer values of n.

Deduce from these results that $\displaystyle \sum_{r=1}^{n}(\frac{1}{(r+1)^3})$ is LESSER than $\displaystyle \frac{1}{4}$.

i can do the first part of the question. i need help for the second and third parts in getting started.