"Write the series and find the sum of..." solved and explained

lwfrgin

Answered question

2021-03-09

Write the series and find the sum of the series of sigma notation.

\sum_{i = 0}^{6} \frac{i}{i - 1}

stuth1

Skilled2021-03-10Added 97 answers

The given series is

\sum_{i = 0}^{6} \frac{i}{i - 1}

Expand the given series as follows.

\sum_{i = 0}^{6} \frac{i}{i - 1} = \frac{0}{0 - 1} + \frac{1}{1 - 1} + \frac{2}{2 - 1} + \frac{3}{3 - 1} + \frac{4}{4 - 1} + \frac{5}{5 - 1} + \frac{6}{6 - 1}

= 0 + \frac{10}{+} \frac{21}{+} \frac{32}{+} \frac{43}{+} \frac{54}{+} \frac{65}{}

= \frac{10}{+} \frac{21}{+} \frac{32}{+} \frac{43}{+} \frac{54}{+} \frac{65}{}

Thus, the expanded form of the given series is

\frac{10}{+} \frac{21}{+} \frac{32}{+} \frac{43}{+} \frac{54}{+} \frac{65}{}

Simplify further and evaluate the sum of the series as follows.

\sum_{i = 0}^{6} = \frac{10}{+} \frac{21}{+} \frac{32}{+} \frac{43}{+} \frac{54}{+} \frac{65}{}

= undefined + \frac{21}{+} \frac{32}{+} \frac{43}{+} \frac{54}{+} \frac{65}{} (\frac{10}{=} undefined or \infty)

=undefined
Thus, the sum of the given series is not defined.

Jeffrey Jordon

Expert2021-12-27Added 2605 answers

Answer is given below (on video)

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