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