What is the solution to ΣΣ(sinx)(cosx)?

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Discussion Overview

The discussion revolves around the mathematical expression ΣΣ(sinx)(cosx), specifically addressing the summation variables and convergence of the series. Participants explore the nature of the summation, its intended form, and the implications of the trigonometric functions involved.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • Some participants question the clarity of the original question, particularly regarding the variables being summed and their roles in the summand.
  • There is a suggestion that the intended expression might be Σ_{n=0}^∞ Σ_{m=0}^∞ sin(n)cos(m), although this is not confirmed.
  • One participant argues that the proposed sum does not converge, citing that there are arbitrarily large values of m and n for which |sin(n)cos(m)| approaches 1.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the original question's clarity or the convergence of the proposed sum, indicating multiple competing views and unresolved aspects of the discussion.

Contextual Notes

The discussion highlights potential ambiguities in the notation and the need for clearer definitions of the summation indices. The convergence issue remains unresolved, with differing opinions on the behavior of the series.

abhaiitg
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what is the solution to this ?
∞∞
ΣΣ(sinx)(cosx)=??
00
 
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Your question isn't clear. What variables are you summing over? And where do those appear in the summand?
 
Xevarion said:
Your question isn't clear. What variables are you summing over? And where do those appear in the summand?

Are one of the trig functions supposed to be a function of y?
 
Since there was no y mentioned in the entire post, apparently not! But Xevarion's point is more than that. Typically "x" (or "y") in a function represents a continuous variable- but the sums must be over discrete indicies.

Perhaps it was
[tex]\sum_{n= 0}^\infty \sum_{m= 0}^\infty sin(n)cos(m)[/tex]
that was intended. But the only way we will know for sure is if abhaaiitg tells us!
 
yeah it was as u think
 
That sum doesn't converge. There are arbitrarily large $m, n$ with $|\sin(n)\sin(m)|$ close to 1.
 

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