Question

Find the sum:
$2+4+6+.......+200$

Answer 1

We know that form$2$ to $100$ there are $50$ odd and $50$ even numbers

same with $102$ to $200$.

So in from $2$ to $200$, there are $100$ even numbers.

So $n=100$

now we also know that the sum of even numbers starting from $2$ to $n$ terms is given by, $n(n+1)$

Plugging in the value of $n$,

We get,

1$00\times 101$

$10100$.

Thus the sum is $10100$.