Menu Close

Solve-for-natural-numbers-31-k-1-n-n-k-m-1-n-m-n-k-31-30-




Question Number 187373 by Shrinava last updated on 16/Feb/23
Solve for natural numbers:  31 + Σ_(k=1) ^n  ( ((n),(k) )  ∙ Σ_(m=1) ^n  m^(n−k) ) = 31^(30)
$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{natural}\:\mathrm{numbers}: \\ $$$$\mathrm{31}\:+\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\left(\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}\:\:\centerdot\:\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{m}^{\boldsymbol{\mathrm{n}}−\boldsymbol{\mathrm{k}}} \right)\:=\:\mathrm{31}^{\mathrm{30}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *