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advanced-cslculus-prove-that-n-0-1-16-n-4-8n-1-2-8n-4-1-8n-5-1-8n-6-pi-




Question Number 131711 by mnjuly1970 last updated on 07/Feb/21
       advanced  cslculus ..    prove  that:    Σ_(n=0 ) ^∞ (1/(16^n ))((4/(8n+1))−(2/(8n+4))−(1/(8n+5))−(1/(8n+6)))=π
$$\:\:\:\:\:\:\:{advanced}\:\:{cslculus}\:.. \\ $$$$\:\:{prove}\:\:{that}: \\ $$$$\:\:\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{n}} }\left(\frac{\mathrm{4}}{\mathrm{8}{n}+\mathrm{1}}−\frac{\mathrm{2}}{\mathrm{8}{n}+\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{6}}\right)=\pi \\ $$
Commented by JDamian last updated on 07/Feb/21
Please, how many indices are there? k? n?
$${Please},\:{how}\:{many}\:{indices}\:{are}\:{there}?\:{k}?\:{n}? \\ $$

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