Solve the following sum:

$latex \sum_{n=1}^{100}2n+3$

[Maximum mark: 2]$latex \sum_{n=1}^{100}2n+3 = 2\sum_{n=1}^{100}n + \sum_{n=1}^{100}3$

We apply the formula $latex \sum_{n=1}^{100}n = \frac{n \left ( n+1 \right ) }{2} = 5050$.

So $latex \sum_{n=1}^{100}2n+3 = 2 \cdot 5050 + 3 \cdot 100 = 10400$.