A Telescoping Power Sum

★ 6/10Arithmetic Progression sequences Telescoping

Problem

An arithmetic sequence $\{a_n\}$ has its first term equal to its common difference, and its partial sums $S_n$ satisfy $S_{10} = 55$ . A sequence $\{b_n\}$ satisfies $b_1 = 1$ and, for $n \geqslant 2$ ,

b_n = \frac{2^{n-1}a_{n-1}}{2S_n}.

If $T_n$ denotes the sum of the first $n$ terms of $\{b_n\}$ , find $T_{100}$ .

Answer

Solution

Difficulty	6/10
Topics	Arithmetic Progression, sequences, Telescoping

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