We can see from the series that

`a_n=1/(2n-1)`

`b_n=((-1)^n)/(2n)`

Now, using `C_n=sqrt((a_n)^2+(b_n)^2)` for each term, we have:

`a_n=1/(2n-1)` `b_n=((-1)^n)/(2n)` `C_n=sqrt((a_n)^2+(b_n)^2)`
`a_1=1` `b_1=-1/2` `C_1=sqrt(1^2+(-1/2)^2)=1.118`
`a_2=1/3` `b_2=1/4` `C_2=sqrt((1/3)^2+(1/4)^2)=0.4167`
`a_3=1/5` `b_3=-1/6` `C_3=sqrt((1/5)^2+(-1/6)^2)=0.260`
`a_4=1/7` `b_4=1/8` `C_4=sqrt((1/7)^2+(1/8)^2)=0.190`

The resulting line spectrum is:

12340.20.40.60.811.2nCOpen image in a new page

The line spectrum for the function `f(t)`.

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