(-1)^n+1 x n = 50

n = 51

$${\left(-{\mathtt{1}}\right)}^{{\mathtt{51}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{51}} = {\mathtt{50}}$$

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That is neat Alan  

Notice that this wouldn't be too difficult to solve........the first term is either -1 or 1.....

Let's suppose it was 1.....then "n" would have to be even........rearranging the equation, we have

n = 50 - 1   = 49.......but this is a contradiction, because n is even

If n were odd, we would have {again, rearranging}

n = 50 + 1........and this must be the solution, because  

(-1)^51 + 51 = 50     →  -1 + 51  = 50     ..... which is true.....!!!