i know it's not very complicated, i just need help understanding this one

$\displaystyle lim(1/1*2+1/2*3+...+1/(n*(n+1)))= ?$

n->inf

i already know the answer is 1, and i can see how the fractions are adding up to something that is <1 but i don't know how to get to that conclusion

sorry i still don't know how to use latex, it will be different on my next posts

thanks!