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**shah4u19** What is the sum of the series 1/ (n x (n+2)) from n=2 as n--> infinity? This series does converge because limit of this is 0. I know that the partial function is (1/2n)- (1/(2(n+2))). Then when I take a look at which way the series go, I end up with S of n = (1/12) - (1/(2(n+2))) - (1/(2(n+2))). I take a limit of (1/12) - lim as n-->infinity of (1/(2(n+2))) - lim as n-->infinity of (1/(2(n+2)))= (1/12)-0-0=(1/12). I don't know where to go after that.

Also how do you find limit from n=1 as n --> infinity of (1/((n)^(1/2)))-(1/((n+1)^(1/2)))? I know this one also converges because limit of this is 0.

Thanks!