Find the sum of consecutive terms of a geometric sequence Calculus

Let u_n be the sequence defined as u_n=3\times 2^n.

Calculate \sum_{k=2}^7u_k.

\sum_{k=2}^7u_k=756

\sum_{k=2}^7u_k=24

\sum_{k=2}^7u_k=88

\sum_{k=2}^7u_k=1\ 188

Let u_n be the sequence defined as u_n = \dfrac{2}{2^n}.

Calculate \sum_{k=2}^{8} u_k.

\sum_{k=2}^{8} u_k=\dfrac{127}{128}

\sum_{k=2}^{8} u_k=\dfrac{255}{256}

\sum_{k=2}^{8} u_k=254

\sum_{k=2}^{8} u_k=\dfrac{127}{256}

Let u_n be the sequence defined as u_n = \dfrac{1}{3} \times \left(\dfrac{5}{4}\right)^n.

Calculate \sum_{k=1}^{4} u_k.

\sum_{k=1}^{4} u_k=\dfrac{615}{256}

\sum_{k=1}^{4} u_k=\dfrac{305}{192}

\sum_{k=1}^{4} u_k=\dfrac{123}{64}

\sum_{k=1}^{4} u_k=\dfrac{369}{256}

Let u_n be the sequence defined as u_n = 6 \times 4^n.

Calculate \sum_{k=4}^{7} u_k.

\sum_{k=4}^{7} u_k=130\ 560

\sum_{k=4}^{7} u_k=32\ 256

\sum_{k=4}^{7} u_k=129\ 024

\sum_{k=4}^{7} u_k=510

Let u_n be the sequence defined as u_n = 3 \times \left(\dfrac{2}{3}\right)^n.

Calculate \sum_{k=3}^{9} u_k.

\sum_{k=3}^{9} u_k=\dfrac{16\ 472}{6\ 561}

\sum_{k=3}^{9} u_k=\dfrac{153\ 368}{59\ 049}

\sum_{k=3}^{9} u_k=\dfrac{4\ 118}{2\ 187}

\sum_{k=3}^{9} u_k=1\ 016

Let u_n be the sequence defined as u_n = 5 \times 2^{2n}.

Calculate \sum_{k=1}^{6} u_k.

\sum_{k=1}^{6} u_k=27\ 300

\sum_{k=1}^{6} u_k=109\ 220

\sum_{k=1}^{6} u_k=1\ 260

\sum_{k=1}^{6} u_k=5\ 460

Let u_n be the sequence defined as u_n = \left(\dfrac{2}{3^n}\right)^2.

Calculate \sum_{k=2}^{5} u_k.

\sum_{k=2}^{5} u_k=\dfrac{3\ 280}{59\ 049}