I'm trying to remove the summation sign from this formula, is this possible?
$$1+\sum_{k=1}^{500}(4(2k+1)^2-12k)$$
I'm trying to remove the summation sign from this formula, is this possible?
$$1+\sum_{k=1}^{500}(4(2k+1)^2-12k)$$
Hints: expand $4(2k+1)^{2}-12k$ and use
$$\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$$
$$\sum_{k=1}^{n}k^{2}=\frac{n(n+1)(2n+1)}{6}.$$
You can find a proof of the second formula in this post of mine (in Portuguese).