If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd ...
If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers
Answer/Solution
100
Steps/Work
First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.
Answer: E.
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.
Answer: E.