Evaluate these geometric series:

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

Problem

Evaluate these geometric series: (1) ∑k=1103×2k−1\sum_{k=1}^{10}3\times2^{k-1} (2) ∑k=112(12)k−2\sum_{k=1}^{12}\left(\frac{1}{2}\right)^{k-2} (3) ∑k=1256×(−2)k\sum_{k=1}^{25}6\times(-2)^k

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