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misogynisticfeminist

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**2 math questions (summation, mathematical induction)**

I have 2 questions regarding summation and mathematical induction

2. Prove by mathematical induction

[tex] \sum^n_{r=1} \frac {1}{r(r+2)} = \frac {3}{4} - \frac {(2n+3)}{2(n+1)(n+2)} [/tex]

i am now trying to prove that

[tex] 3/4 - \frac{2(n+1)+3}{2(n+2)(n+3)} - \frac {1}{n+1}{n+3} [/tex]

I seem to get caught up with the algebra and what i get is

[tex] \frac {2n^2+5n+1}{2(n+1)(n+2)(n+3)} [/tex]. instead of [tex] \frac {2n^2+5n+3}{2(n+1)(n+2)(n+3)} [/tex]

3. Prove by induction that [tex] \sum^n_{r=1}rx^{r-1}=\frac{1-(n+1)x^n+nx^{n+1}}{(1-x)^2} [/tex]

again, I'm caught up with the algebra.

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