Finding the sum of 1/(n*(n+1)) series to solve the limit

[transgalactic]

[SOLVED] limit question

i added a file with the question and how i tried to find the legality between the
objects of the series

lim [1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n*(n+1))]
n>>infinity


i can't find the total sum of all the objects in the series

if i would get the total sum of all the objects
i can get the limit

i could add the first numbers and to make an estimation about the limit
but how i solve it in equetions??

 

[TD]

Does this help?

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

 

[transgalactic]

i got

lim 1- [1/(n-1)] =1
n>>infinity


thanks

 

[TD]

The limit is indeed 1.