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Question Number 145451 by math55 last updated on 05/Jul/21

$$\underset{n=1}{\sum ^{\mathrm{\infty }}}{(-1)}^{n-1}\frac{{30}^{2n-1}}{(2n-1)!}$$

Answered by Olaf_Thorendsen last updated on 05/Jul/21

$$\mathrm{S}=\underset{n=1}{\sum ^{\mathrm{\infty }}}{(-1)}^{n-1}\frac{{30}^{2n-1}}{(2n-1)!}$$$$\mathrm{S}=\underset{n=0}{\sum ^{\mathrm{\infty }}}{(-1)}^n\frac{{30}^{2n+1}}{(2n+1)!}$$$$\mathrm{S}=\sin \left(30\right)$$$$\mathrm{If}\mathrm{is}30°,\mathrm{S}=\frac{1}{2}$$

Commented by math55 last updated on 05/Jul/21

please sir is there anyway to prove that it's 1/2 without passing through sin30°

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