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A sequence has nth term given by T n =(n 2 +1)n! . Find summation (sigma) T n .

A sequence has nth term given by Tn=(n2+1)n!. Find summation (sigma) Tn.

Grade:12th pass

1 Answers

basil mansuri
18 Points
11 months ago
Since according to your question the Nth term is i.e. Tn= (n^2+1)n.
Apply the special series and sequence formula you will get your answer.
 
Tn = (n^2+1)n = n^3+n
 
Sn= sigma(k=1 to k = n) k^3+ sigma(k=1 to k=n) k
 
Sn= [ n(n+1)/2)]^2 + n(n+1)/2
Sn= n(n+1)/2 * [n(n+1)/2 + 2]
Sn= n(n+1)(n^2+n+2)/4
Hence thats your answer. Thank you very much.
 

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