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Question
Sum of n terms of the series whose nth term is 2n−1+8n3−6n2.
Sum of n terms of the series whose nth term is 2n−1+8n3−6n2.
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Solution
Let the sum be denoted by S; then
S=∑2n−1+8∑n3−6∑n2
=2n−12−1+8n2(n+1)24−6n(n+1)(2n+1)6
=2n−1+n(n+1){2n(n+1)−(2n+1)}
=2n−1+n(n+1)(2n2−1).
S=∑2n−1+8∑n3−6∑n2
=2n−12−1+8n2(n+1)24−6n(n+1)(2n+1)6
=2n−1+n(n+1){2n(n+1)−(2n+1)}
=2n−1+n(n+1)(2n2−1).
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