Question 1035847: When the sun if the first 31 positive even integers is added to the first 32 positive off integers the result is N find N Answer by ikleyn(52884) (Show Source):
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When the sun if the first 31 positive even integers is added to the first 32 positive odd integers the result is N. Find N.
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The sum of the first 31 positive even integers is the sum
2 + 4 + 6 + . . . + 62. (1)
The sum of the first 32 positive odd integers is the sum
1 + 3 + 5 + . . . + 63. (2)
When these two sums, (1) and (2) are added, the sum is
1 + 2 + 3 + 4 + 5 + 6 + . . . + 63. (3)
It is the sum of the first 63 positive integers.
It is equal to = 63*32 = 2016.
You can use the formula for the sum of an arithmetic progression (see the lesson Arithmetic progressions in this site)
or use the fact that the sum of the first "n" positive integer numbers is
See the same lesson or/and the following two lessons
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
in this site.
