Question 1035847
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When the sun if the first 31 positive even integers is added to the first 32 positive {{{highlight(cross(off))}}} 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*64)/2}}} = 63*32 = 2016.


You can use the formula for the sum of an arithmetic progression (see the lesson <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A> in this site) 

or use the fact that the sum of the first "n" positive integer numbers is    {{{(n*(n+1))/2}}}


See the same lesson or/and the following two lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A> 

in this site.
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