1. ## Finding a formula

1. Find a formula for
1/(1x2) + 1/(2x3)+...+ 1/n(n+1) by examining values for small values of n.

2. prove the formula

-why am I being asked to find a formula? is the summation of all values of n up to i (the formula given) not sufficient?

thanks

2. Is...

$\displaystyle \displaystyle \frac{1}{n\ (n+1)} = \frac{1}{n} - \frac{1}{n+1}$ (1)

... so that...

$\displaystyle \displaystyle \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \dots + \frac{1}{n \cdot (n+1)} = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \dots + \frac{1}{n} - \frac{1}{n+1} = 1 -\frac{1}{n+1}$ (2)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. Originally Posted by mremwo
1. Find a formula for
1/(1x2) + 1/(2x3)+...+ 1/n(n+1) by examining values for small values of n.

2. prove the formula

-why am I being asked to find a formula? is the summation of all values of n up to i (the formula given) not sufficient?

thanks

Hint: $\displaystyle \frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}$

Tonio