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When is this sum nonzero?
The Next CEO of Stack OverflowWhen is this sum equal to $0$?Value of this infinite sumFind the sum of this seriesWhy is this sum zero?How to telescope this sumDoes this sum have any meaning?Determining the Fourier Series and its convergenceHow to calculate this sum.simplifying this sumWhen is the sum non-zero?
$begingroup$
I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:
beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation
However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great
summation
asked Mar 19 at 22:08
MatthewMatthew
337112
$endgroup$
add a comment |
$begingroup$
I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:
beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation
However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great
summation
asked Mar 19 at 22:08
MatthewMatthew
337112
$endgroup$
$begingroup$
any constraint on $n$?
$endgroup$
– MoonKnight
Mar 20 at 0:10
add a comment |
$begingroup$
I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:
beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation
However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great
summation
asked Mar 19 at 22:08
MatthewMatthew
337112
$endgroup$
I am doing a problem whereby the proof is finished if I can find positive integers $h,h'$ such that:
beginequation sum_j=0^2n-1(-1)^j[cos((h+h')j fracpin) + cos((h-h')j fracpin)] neq 0 endequation
However I simply cannot find a way where this sum is nonzero, so I feel I may have constructed the proof incorrectly to lead to this requirement. I converted the equation into complex exponential however that didn't help me. Moreover wolfram alpha says it is zero. Any help would be great
summation
summation
asked Mar 19 at 22:08
MatthewMatthew
337112
asked Mar 19 at 22:08
MatthewMatthew
337112
asked Mar 19 at 22:08
MatthewMatthew
337112
asked Mar 19 at 22:08
MatthewMatthew
337112
asked Mar 19 at 22:08
MatthewMatthew
337112
337112
$begingroup$
any constraint on $n$?
$endgroup$
– MoonKnight
Mar 20 at 0:10
add a comment |
$begingroup$
any constraint on $n$?
$endgroup$
– MoonKnight
Mar 20 at 0:10
$begingroup$
any constraint on $n$?
$endgroup$
– MoonKnight
Mar 20 at 0:10
$begingroup$
any constraint on $n$?
$endgroup$
– MoonKnight
Mar 20 at 0:10
add a comment |
0
active
oldest
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$begingroup$
any constraint on $n$?
$endgroup$
– MoonKnight
Mar 20 at 0:10