Question: 1.) (20 points) Prove, using induction, that $$ sum_{k=2}^{N} frac{1}{(k-1) (k+1}=frac{(N-1)3 N+2)}4 N(N+1)} $$ is true for all natural numbers $N geq 1$. SE. SD.0311

$1.) (20 points) Prove, using induction, that $$ \sum_{k=2}^{N} \frac{1}{(k-1) (k+1}=\frac{(N-1)3$

1.) (20 points) Prove, using induction, that $$ \sum_{k=2}^{N} \frac{1}{(k-1) (k+1}=\frac{(N-1)3 N+2)}4 N(N+1)} $$ is true for all natural numbers $N \geq 1$. SE. SD.0311

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