Verify that for any non-zero real constant, $m$, $\frac{1}{m}\left( \frac{1}{mr+1-m}-\frac{1}{mr+1}

Question

Verify that for any non-zero real constant, $m$, $\frac{1}{m}\left( \frac{1}{mr+1-m}-\frac{1}{mr+1} \right)=\frac{1}{\left( mr+1-m \right)\left( mr+1 \right)}$. [1] Hence, show that $\sum\limits_{r=1}^{n}{\frac{1}{\left( mr+1-m \right)\left( mr+1 \right)}=\frac{n}{mn+1}}$. [3] $\frac{1}{1\cdot 3}+\frac{1}{1\cdot 4}+\frac{1}{3\cdot 5}+\frac{1}{4\cdot 7}+\frac{1}{5\cdot 7}+\frac{1}{7\cdot 10}+...+\frac{1}{39\cdot 41}+\frac{1}{58\cdot 61}$. [4]

Accepted Answer

$\frac{2040}{2501}$

2007 HCI C1 Lecture Test Q6 [Modified]

2007 HCI C1 Lecture Test Q6 [Modified]

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