41) Given exprsn = Lt n-->∞ sin (na)/n
= Lt n-->∞ [ sin(na)/na x a ]
Is Lt for n or a ????
1)Evaluate \sum_{0}^{infinity}{sin(n\alpha )/n} = ??? (n varies from 0 to infinity)
[\alpha\varepsilon (0,2\pi )]
2)Find the sum of \sum_{r=00}^{infity}{\frac{sinr\alpha }{sin^{r}\alpha }}
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3 Answers
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62first one can be solved by first using
\sum_{0}^{infinity}{sin(n x )/n} = \sum_{0}^{\infty}{\int cos(nx)dx}=\int ( \sum_{0}^{\infty}{cos(n\alpha)})dx
The infinite sum of cos can by found out using complex numbers.. or even otherwise..