Adding a series of doubles

1. Have a friend choose a a single digit number. (No restrictions for experts.)
2. Ask your friend to jot down a series of doubles (where the next term is always double the preceding one), and tell you the last term.
3. Ask your friend to add up all these terms.
4. You will give the answer before he or she can finish: The sum of all the terms of this series will be two times the last term minus the first term.

   Example:

1. If the number selected is 9:
2. The series jotted down is: 9, 18, 36, 72, 144.
3. Two times the last term (144) minus the first (9):
   2 x 144 = 288; 288 - 9 = 279.
4. So the sum of the doubles from 9 through 144 is 279.

   See the pattern? Here's one for the experts:

1. The number selected is 32:
2. The series jotted down is: 64, 128, 256, 512.
3. Two times the last term (512) minus the first (64):
   2 x 512 = 1024; 1024 - 32 = 1024 - 30 - 2 = 994 - 2 = 992.
4. So the sum of the doubles from 32 through 512 is 992.

Remember to subtract in steps from left to right.
With practice you will be expert in summing series.