Express the series 32 – 20 33 - 21 3k+1 – 2k-1 + 51 52 using...

Question

Question

Answer 1

Answer #1

Clearly, the k th term of the given series is

$\frac{3^{k+1}-2^{k-1}}{5^{k}}$ $for\ k=1,2,3,...$

Therefore, the given series can be expressed using sigma notation as

$\frac{3^{2}-2^{0}}{5^{1}}+\frac{3^{3}-2^{1}}{5^{2}}+...+\frac{3^{k+1}-2^{k-1}}{5^{k}}+...=\sum_{k=1}^{\infty}\frac{3^{k+1}-2^{k-1}}{5^{k}}$

Answer 2

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