Tricks on getting the sum of all odd numbers from 1 through a 2-digit odd number:
- Choose 2-digit odd number then add one (1).
- Divide the sum by 2 (or multiply by 1/2).
- Square the result of Step 2. This is now the sum of all odd numbers from 1 through the 2-digit number chosen.
Example:Add the odd numbers from 1-83
Step 1: 83 + 1 = 84
Step 2: 84÷ 2 = 42
Step 3: 42² = 1764
Therefore, the sum of all the odd numbers from 1 through 83 is
1764.
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Tricks on getting the sum of all even numbers from 2 through a 2-digit even number:
- Choose 2-digit even number.
- Divide the even number by 2 (or multiply by 1/2).
- Multiply the result by the number next to it.
Example:Find the sum of even numbers from 2 to 36.
Step 1: 36 is the 2 digit even number
Step 2: 36 ÷ 2 = 18
Step 3: 18 x 19 = 342
(The number next to 18 is 19. Multiply this to the result in step 2.)
Therefore, the sum of all the even numbers from 2 through 36 is
342.
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