Is there a formula for this summation $\sum\limits_{k=i}^\mathbb{N}{i}$?

Question

Is there a formulae for this summation? I wonder this could be not a constant or to say that i * i?

$\sum\limits_{k=i}^\mathbb{N}{i}$

Answer 1

$$\sum\limits_{k=i}^N i = i \sum\limits_{k=i}^N 1 = i(N - i + 1)$$

Maybe you meant: $$\sum\limits_{k=i}^N k = \sum\limits_{k=1}^N k - \sum\limits_{k=1}^{i-1}k = \frac{N(N+1)}2 - \frac{i(i-1)}2$$