Skip over navigation
Look at the sequence below:
$1, 2, 4, 8, 16...$
Can you describe how to get from one term to the next?
Can you describe the $n^{th}$ term of the sequence?
Now try adding together terms from the sequence:
$1 + 2$
$1 + 2 + 4$
$1 + 2 + 4 + 8$
Do you notice anything interesting?
Can you predict what $1 + 2 + 4 + ... + 64 + 128$ would be? Check to see if you are right.
How could you write the answer to $1 + 2 + 4 + ... + 2^n$?
Justify why your formula works.
Classic Problem - Tower of Hanoi
Age 14 to 16
Challenge Level 
Look at the sequence below:
$1, 2, 4, 8, 16...$
Can you describe how to get from one term to the next?
Can you describe the $n^{th}$ term of the sequence?
Now try adding together terms from the sequence:
$1 + 2$
$1 + 2 + 4$
$1 + 2 + 4 + 8$
Do you notice anything interesting?
Can you predict what $1 + 2 + 4 + ... + 64 + 128$ would be? Check to see if you are right.
How could you write the answer to $1 + 2 + 4 + ... + 2^n$?
Justify why your formula works.