Find the sum to 'n' terms in the following series
1. 1.2 + 2.3 + 3.4 + ...........
2. 2.3.4 + 3.4.5 + ...........
Tejaswi Kasturi
(student-cpt)
(427 Points)
Replied 08 June 2012
the kth term of the 1st question is k(k+1)= k^2 + k sum of n terms is n(n+1)(2n+1)/6 + n(n+1)/2 = n(n+1)(n+2)/3
the kth term of the 2nd equation is (k+1)*(k+2)*(k+3) = k^3 + 6k^2 + 11k + 6 sum to n terms is n^2*(n+1)^2/4 + n*(n+1)*(2n+1) + 5.5n*(n+1)+6n = n*(n+5)*(n^2 + 5*n + 10)/4
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