I’m given a very elementary problem. Solve the following summation for $n=100$:
$$\Sigma_{k=1}^n (5-4k)$$
Which I solve as follows:
$$\Sigma_{k=1}^n 5 - 4\Sigma_{k=1}^n k$$
Which simplifies to:
$$5n - 4 ( \frac{n(n+1)}{2})$$
Or:
$$6n - 2n^2$$
So, I get the answer $-19400$ using this formula. However, when I use WolframAlpha to solve the summation as given, I get $-19700$. What’s going on?
$$5n-4\left(\frac {n(n+1)}2\right) = 5n-2(n^2+n) = 3n-2n^2$$