r=1∑n[1+cos(2n(2r−1)π)][5+3cos(2n(2r−1)π)]21−cos(2n(2r−1)π)=16n(8n−11)
Prove that for integer n>1, the equation above holds true.
Please try not to use induction (assuming it's possible).
This problem was copied from another math forum but no one responded to it.
This is a part of the set Formidable Series and Integrals.
#Calculus
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@Aditya Kumar bache ki jaan lo ge kya thoda to hint de the Bhaiya.
have you tried roots of unity
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How does that help? We can only use that if we can split out all the expressions and calculate them separately. ∑g⋅hf=∑f⋅∑g1⋅∑h1.
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I havent tried this yet but we could use partial fractions and then f'/f or maybe chebyshev polynomials of the first kind.....