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NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 77 of 106
Marks: +1, -0
n2+2nn^2 + 2^n
Solution:  
We have, ana_n = n2+2nn^2 + 2^n
Hence, the sum to n terms is,
SnS_n = ∑k=1nak\sum_{k=1}^{n} a_k = ∑k=1n(k2+2k)\sum_{k=1}^{n} (k^2+2^k) = ∑k=1nk2+∑k=1n2k\sum_{k=1}^{n} k^2 + \sum_{k=1}^{n} 2^k
= n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6} + (2+22+23+...+2n)(2+2^2+2^3+...+2^n) = n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6} + 2(2n−1)2(2^n-1)
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