SOLUTION: Find the sum of the first 100 odd numbers minus the sum of the first 100 numbers
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Question 278912: Find the sum of the first 100 odd numbers minus the sum of the first 100 numbers
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The sum of the first 100 odd numbers:
The sum of the first 100 numbers:
The first 100 odd minus the first 100
\ -\ \sum_{i=1}^{100}\,\left(i\right)\ =\ \sum_{i=1}^{100}\,\left(2i\ -\ 1\right)\ -\ \left(i\right)\ = \ \sum_{i=1}^{100}\,\left(i\ -\ 1\right))
The first term of the resulting series (
) is 
The last term of the resulting series (
) is 
And there are still 
terms, so the sum is:
\left(n\right)}{2}\ =\ \frac{(0\ +\ 99)(100)}{2}\ =\ 99\,\cdot\,50\ =\ 4950)
Verification that
and
and therefore
\ -\ \sum_{i=1}^{100}(i)\ =\ 10000\ -\ 5050\ =\ 4950)
is left as an exercise for the student.
John
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