0
$\begingroup$
  1. Expand in Fourier series of $f(x) = \sin x$ for $0. Deduce the result \[ \frac1{1 \cdot 3} - \frac{1}{3\cdot5} +\frac{1}{5\cdot 7} - \cdots = \pi-\frac{2}{4}. \]

  2. Obtain half range sine series for $f(x)$ in $0 and deduce the series \[\sum\frac{1}{n^2} = \frac{{\pi^2}}6.\]

  • 2
    Perhaps you should explain what you have tried already?2012-07-20
  • 0
    I tried to fix the source and tags — whatever you typed wasn't displaying at all on my end, so I tried to put everything in LaTeX. Please check for errors. [It's a good idea to try to learn the rudiments of LaTeX for the purpose of asking questions here, by the way.] In particular, I couldn't tell what you were trying to write in that first series. It doesn't look right to me as it is.2012-07-20
  • 0
    Presumably, the term $\frac 1 {3\cdot 7}$ is meant to be $\frac 1 {5\cdot 7}$, or else I don't see the pattern to the series.2012-07-20
  • 0
    @ThomasAndrews Change made.2012-07-20
  • 0
    @ThomasAndrews I hv the same question as it is written....May be there is a printing mistake...Please can you provide me the steps of the solution taking 1/5.7 if you think its correct....and the steps for the second part too....please....2012-07-20
  • 0
    Your LHS is 0.783731515 (considering first 150 terms) while your RHS is 2.641592654. Please check . Your RHS should be $\frac{\pi}{4}- \frac{1}{2}$ - for the first series2012-07-21

1 Answers 1