Evaluating Series

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Evaluating Series (1) Evaluate the series 36+64+100+144+⋯+10,00036 + 64 + 100 + 144 + \dots + 10,000 (2) Evaluate ∑j=2∞∑k=1∞(12)j(13)k\sum_{j=2}^{\infty} \sum_{k=1}^{\infty} \left(\frac{1}{2}\right)^j \left(\frac{1}{3}\right)^k. If you rewrite this as a different, equivalent sigma expression, you must justify your reformulation.

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