Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Simple additions can lead to intriguing results...
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? $1 + 2 + 3 + \dots + (n - 1) + n$