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The Fourier series expansion of the saw-toothed waveform f(x) = x in (- π, π) of period 2π gives the series, 
The sum is equal to
The sum is equal to
- a)π/2
- b)π2/4
- c)π2/16
- d)π/4
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The Fourier series expansion of the saw-toothed waveform f(x) = x in (...
Concept:
If f(x) is periodic function of period ‘’T’’ then f(x) can be expressed as below:
If f(x) is odd function, then only the coefficients of sin nx exists (i.e. an = 0 & a0 = 0).
Calculation:
We are given f(x) = x for x ∈ (-π, π)
sin a f(x) = x is odd So, an = 0, a0 = 0
So, now we have to find bn,
Hence required sum of series is
Alternate Method:
Taylor expansion of tan-1x is expressed in below:
Put x = 9, above expansion series
Hence π/4 is required sum of series.
If f(x) is periodic function of period ‘’T’’ then f(x) can be expressed as below:
If f(x) is odd function, then only the coefficients of sin nx exists (i.e. an = 0 & a0 = 0).
Calculation:
We are given f(x) = x for x ∈ (-π, π)
sin a f(x) = x is odd So, an = 0, a0 = 0
So, now we have to find bn,
Hence required sum of series is
Alternate Method:
Taylor expansion of tan-1x is expressed in below:
Put x = 9, above expansion series
Hence π/4 is required sum of series.
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The Fourier series expansion of the saw-toothed waveform f(x) = x in (- π, π) of period 2π gives the series,The sum is equal toa)π/2b)π2/4c)π2/16d)π/4Correct answer is option 'D'. Can you explain this answer?
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