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Sum of the first $n$ natural numbers

How do I calculate the sum of the first $n$ natural numbers?
So far I have $\frac{n(n+1)}{2}$ + 1, but I’m not sure if that’s right.

A:

Yes it is correct. This is a proof by induction.
Let $a_1,a_2,..,a_k$ be the first $k$ natural numbers (as
listed by the OP) and let’s say that $a_k$ is the $k$-th natural number.
Then, since $a_k$ is the $k$-th natural number, we also have $a_k = 1 + 2 + 3+…+k$
This means that
$$k(k+1) = 1 + 2 + 3 +…+k + (k+1)k$$
which is the case when we sum the first $k+1$ natural numbers.
Thus, by induction, we have that
$$\sum_{k=1}^n k(k+1) = \sum_{k=1}^n k + k^2 = \frac{n(n+1)}{2} + 1$$
and we have that the sum of the first $n$