This is my first proof by induction so I need some assistance
If n is a positive integer, then [tex]\sum1/(k(k+1))[/tex]from k=1 to n is equal to n/(n+1)
I'm not sure if this is useful for this proof but we are given the proposition:
let n be a positive integer. Then the sum of the first n positive integers is equal to (n(n+1))/2.
The Attempt at a Solution
(1) Let S be the set of all positive integers k such that 1/2+1/6+...+1/k(k+1)= n/(n+1)
(2) 1 is in S because 1/1(1+1)=1/2 which is in S (not sure if this is the correct approach)
(3) Let n be any element of S and let t=n+1
Am I on the right track? For my next step would I just substitute t=n+1 and solve?