Chapter 11.4, Problem 9WE

To determine

To calculate:

Given series using sigma notation.

Answer to Problem 9WE

Given series $2+4+6+\mathrm{..}+1000$ using sigma notation is ${\displaystyle \sum _{k=2}^{1000}2n}$ .

Explanation of Solution

Give information:

Expression:

  $2+4+6+\mathrm{..}+1000$

It is given that,

  $2+4+6+\mathrm{..}+1000$

Need to rewrite the series $2+4+6+\mathrm{..}+1000$ using sigma notation,

Rewriting the given series by factoring $2$ for each term,

  $2\left(1+2+\mathrm{3..500}\right)$

Here, general term of the given series is $2n$

Representation of the series by sigma notation by taking index $k=2$ to $k=1000$ as

  $2+4+6+\mathrm{..}+1000={\displaystyle \sum _{k=2}^{1000}2n}$

Therefore, Given series $2+4+6+\mathrm{..}+1000$ using sigma notation is ${\displaystyle \sum _{k=2}^{1000}2n}$ .