Simple concept , complicated equation (2)

Calculus Level 4

$\large \sum_{k=1}^{2016}(x+y+k)^{k} = (x+y)^{2017}$

$\large 1-\sum_{k=1}^{2015}\left.\frac{dy}{dx}\right|_{x=k} = \, ?$

The answer is 2016.

1 solution

Simona Vesela
Aug 30, 2016

if we set $x+y = z$ then, after solving the equation, we find that $z=c$ is the solution(I do not know how to prove there are any). Then we have $x+y=c$ and finally $\frac{\mathrm d y}{\mathrm d x} = \frac{\mathrm d (c-x)}{\mathrm d x} =-1$ and $1- \sum_{i=1}^{2015}(-1) =2016$ .

Simple concept , complicated equation (2)

The answer is 2016.

1 solution

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