Back to Calculation Tips & Tricks
- even numbers 2 through selected 2-digit evens
- digits of square of repeating ones
- consecutive odds
- consecutive between 2 numbers
- sequence from 1 to selected 2-digit number
- sequence from 1 to selected 1-digit number and back
- sequences in the 10's
- sequences in the 20's
- sequences in the 30's
- sequences in the 40's
- sequences in the 50's
- sequences in the 60's
- sequences in the 70's
- sequences in the 80's
- series of doubles
- series of quadruples
- series of 10 numbers
- 1's repeating, divide by 9, subtract 21
- 8's repeating, divide by 9, subtract 10
- squares of two numbers
- reversing/adding/subtracting 3-digit numbers
- finding 2.5 percent
- finding 5 percent
- finding 15 percent
- finding 20 percent
- finding 25 percent
- finding 33 1/3 percent
- finding 40 percent
- finding 45 percent
- finding 55 percent
- finding 60 percent
- finding 70 percent
- finding 75 percent
a series of doubles
- Have a friend choose a a single digit number. (No restrictions for experts.)
- 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.
- Ask your friend to add up all these terms.
- 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.
- If the number selected is 9:
- The series jotted down is: 9, 18, 36, 72, 144.
- Two times the last term (144) minus the first (9):
2 × 144 = 288; 288 - 9 = 279.
- So the sum of the doubles from 9 through 144 is 279.
See the pattern? Here's one for the experts:
- The number selected is 32:
- The series jotted down is: 64, 128, 256, 512.
- Two times the last term (512) minus the first (64):
2 × 512 = 1024; 1024 - 32 = 1024 - 30 - 2 = 994 - 2 = 992.
- 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.
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29 April 1996
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