Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 159173 by HongKing last updated on 13/Nov/21

Answered by qaz last updated on 14/Nov/21

$$\mathrm{\Omega }=\underset{\mathrm{k}=1}{\sum ^{\mathrm{\infty }}}\arctan \left(\frac{1}{1+(\mathrm{k}+\frac{5}{3})(\mathrm{k}+\frac{8}{3})}\right)$$$$=\underset{\mathrm{k}=1}{\sum ^{\mathrm{\infty }}}\arctan \frac{(\mathrm{k}+\frac{8}{3})-(\mathrm{k}+\frac{5}{3})}{1+(\mathrm{k}+\frac{5}{3})(\mathrm{k}+\frac{8}{3})}$$$$=\underset{\mathrm{k}=1}{\sum ^{\mathrm{\infty }}}(\arctan (\mathrm{k}+\frac{8}{3})-\arctan (\mathrm{k}+\frac{5}{3}))$$$$=\frac{\pi }{2}-\arctan \frac{8}{3}$$

Commented by HongKing last updated on 14/Nov/21

$$\mathrm{Cool}\mathrm{my}\mathrm{dear}\mathbf{S}\mathrm{er},\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com