a)[tex] \frac{^{n+1)}1}{n}- \frac{^{n)}1}{n+1} = \frac{n+1}{n(n+1)} - \frac{n}{n(n+1)} = \frac{1}{n(n+1)} [/tex]
b)Folosim punctul a)
[tex]S= \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} +...+ \frac{1}{2009} - \frac{1}{2010}\\
S=1- \frac{1}{2010}= \frac{2009}{2010} [/tex]
