Can you please convert the following series into summation notation? Write each series in summation notation beginning with

Question

Can you please convert the following series into summation notation?

Write each series in summation notation beginning with k = 1.

1. \frac{1}{2} +\frac{2}{3} +\frac{3}{4} +\frac{4}{5}+\frac{5}{6}2. [tex]-11+12-13+14-15+16

3. 9-16+25-36+49-64

4. 3+\frac{3}{2} +1+\frac{3}{4}+\frac{3}{5}

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Arianna 2 weeks 2021-10-12T10:05:58+00:00 1 Answer 0

Answers ( )

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    2021-10-12T10:07:24+00:00

     

    \displaystyle\\1)\\\\\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}=\boxed{\sum _{k=1}^{5}{\frac{k}{k+1}}}\\\\\\2)\\\\ -11+12-13+14-15+16=\boxed{\sum _{k=1}^{6}{(-1)^k\cdot(10+k)} }

    \displaystyle\\3)\\9-16+25-36+49-64=\boxed{\sum_{k=1}^{6}{(-1)^{k+1}\cdot(k+2)^2}}\\\\\\4)\\\\3+\frac{3}{2}+1+\frac{3}{4}+\frac{3}{5}=\frac{3}{1}+\frac{3}{2}+\frac{3}{3}+\frac{3}{4}+\frac{3}{5}=\boxed{\sum_{k=1}^{5}{\frac{3}{k}}}

     

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