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Find the sum of all odd numbers between ...

Find the sum of all odd numbers between 100 and 200.

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The series formed by odd numbers lying between 100 and 200 is `101+103+105+.....+199`
Here, a=101,
`d=103-101=105-103=2`
Let `a_(n)=199`
`rArr 101+(n-1)2=199`
`rArr (n-1)2=98 rArr n-1=49` ltbtgt `rArr n=50`
Now, `S_(50)=(50)/(2)(101+199)=7500`
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