Question

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》》Can you solve this《《

●●●Find the sum to n terms of the sequence. =》1.3.2^2 + 2.4.3^2 +3.5.4^2+....●●●●

Answer 1

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Answer 2

Answer:

The nth term of the series can be written as:

Tn = n(n+2)(n+1)2

=(n2+2n) (n2+1+2n)=n4 +4n3+5n2+2n

Sum of n terms will be:

Sn=∑n1n4 + 4∑n1n3 +5∑n1n2+2∑n1n =∑n1n4 + 4(nn+12)3+5n(n+1)(2n+1)6+2n(n+1)2 = ∑n1((n)2)2 + 4(nn+12)3+5n(n+1)(2n+1)6+2n(n+1)2=(n(n+1)(2n+1)6)2 + 4(nn+12)3+5n(n+1)(2n+1)6+2n(n+1)2

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