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Find the sum 11^2-1^2+12^2-2^2+13^2-3^2+...

Find the sum `11^2-1^2+12^2-2^2+13^2-3^2+……+20^2-10^2`

Text Solution

Verified by Experts

The correct Answer is:
1400
`11^(2)-1^(2)+12^(2)-2^(2)+13^(2)-3^(2)+…+20^(2)-10^(2)`
`=(1^(2)+2^(2)+3^(2)+….+20^(2))-2(1^(2)+2^(2)+3^(2)+…+10^(2))`
`=(20xx21xx41)/6-2xx(10xx11xx21)/6`
`=(20xx21)/6(41-21)`
=1400
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