Question

sum to n terms with the nth term being n/n+1 ?

Answer 1

Solution:

Here nth term, tn = n(n+1) = n2+n

Sum, S = ∑tn

= ∑(n2+n)

= ∑n2+∑n

= n(n+1)(2n+1)/6 + n(n+1)/2

= [n(n+1)(2n+1) + 3n(n+1)]/6

= (n(n+1)/6)(2n+1+3)

= n(n+1)(2n+4)/6

= 2n(n+1)(n+2)/6

= n(n+1)(n+2)/3

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