Evaluate the following series:

MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Evaluate the following series: (1) ∑k=317(2(k+1)2+3(43)k)=\sum_{k=3}^{17} \left( 2(k+1)^2 + 3 \left( \frac{4}{3} \right)^k \right) = (2) [∑j=115(j5−7j)]−[∑m=115(m5−9)]=[\sum_{j=1}^{15} (j^5 - 7j)] - [\sum_{m=1}^{15} (m^5 - 9)] = (3) ∑k=13(∑m=k+1k+4(m+k))\sum_{k=1}^{3} \left( \sum_{m=k+1}^{k+4} (m+k) \right)

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