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Question Number 97564 by Power last updated on 08/Jun/20

Answered by Rio Michael last updated on 09/Jun/20

$$\mathrm{Ones}\mathrm{our}\mathrm{teacher}\mathrm{put}\mathrm{this}\mathrm{on}\mathrm{the}\mathrm{board},\mathrm{we}\mathrm{puzzeled}\mathrm{even}$$$$\mathrm{the}\mathrm{geniuses}\mathrm{of}\mathrm{our}\mathrm{class}\mathrm{tried}\mathrm{it}\mathrm{out}\mathrm{but}\mathrm{it}\mathrm{turned}\mathrm{out}$$$$\mathrm{even}\mathrm{the}\mathrm{teacher}{\mathrm{couldn}}^{\prime }\mathrm{t}\mathrm{find}\mathrm{a}\mathrm{particular}\mathrm{summation}\mathrm{formula}$$$$\mathrm{which}\mathrm{described}\mathrm{this}\mathrm{series}\mathrm{even}\mathrm{to}\mathrm{an}\mathrm{approximate}.\mathrm{Some}$$$$1945\mathrm{folks}\mathrm{had}\mathrm{tried}\mathrm{this}\mathrm{problem}\mathrm{and}\mathrm{concluded}\mathrm{that}\mathrm{it}\mathrm{can}\mathrm{only}$$$$\mathrm{be}\mathrm{programmed}\mathrm{hence}\mathrm{no}\mathrm{exact}\mathrm{summation}\mathrm{formula}\mathrm{exist}\mathrm{for}\mathrm{it}.$$$$\mathrm{I}\mathrm{tried}\mathrm{it}\mathrm{out}\mathrm{and}\mathrm{noticed}\left(\mathrm{like}\mathrm{others}\right)\mathrm{that}\mathrm{there}\mathrm{is}\mathbf{no}\mathbf{formula}$$$$\mathbf{to}\mathbf{compute}\mathbf{this}\mathbf{sum}!$$$$\mathrm{but}\mathrm{we}\mathrm{can}\mathrm{obtain}\mathrm{a}\mathrm{bound}\mathrm{to}\mathrm{which}\mathrm{this}\mathrm{series}\mathrm{falls}$$$$:n(1+\frac{1}{4(n-1)})<S<n^n(1+\frac{2}{e(n-1)})$$$$\mathrm{please}\mathrm{do}\mathrm{well}\mathrm{to}\mathrm{search}\mathrm{for}\mathrm{the}\mathrm{programming}\mathrm{codes}\mathrm{for}\mathrm{this}\mathrm{series}.$$

Commented by Power last updated on 09/Jun/20

$$\mathrm{thanks}\mathrm{sir}$$

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