Question

Write out the series given by:

Answer 1

When
`n=1`, we have

`\frac n{2n+1}=\frac1{2\cdot1+1}=\frac13`

When
`n=2`, we have

`\frac n{2n+1}=\frac2{2\cdot2+1}=\frac25`

and so on. The series is then

`\displaystyle\sum_(n=1)^6\frac n{2n+1}=\frac13+\frac25+\frac37+\frac49+\frac5{11}+\frac6{13}`