Slick Summing

Slick Summing printable worksheet
 

In the video below, Charlie works out $1+2+3+4+5+6+7+8+9+10$.

Can you see how his method works?

How could you adapt his method to work out the following sums?

$1 + 2 + 3 + \dots + 19 + 20$

$1 + 2 + 3 + \dots + 99 + 100$

$40 + 41 + 42 + \dots + 99 + 100$

Can Charlie's method be adapted to sum sequences that don't go up in ones?

$1 + 3 + 5 + \dots + 17 + 19$

$2 + 4 + 6 + \dots + 18 + 20$

$42 + 44 + 46 + \dots + 98 + 100$

Can you find an expression for the following sum?
$1 + 2 + 3 + \dots + (n - 1) + n$