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Find the value of 1000^2-999^2+998^2-997^2.......+4-1=?

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Find the value of 1000^2-999^2+998^2-997^2.......+4-1=?
posted Sep 2, 2017 by anonymous

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1 Answer

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a^2-b^2 = (a+b)(a-b)
so
100^2-99^2=(100+99)(100-99)=100+99

so
1000^2-999^2+998^2-997^2.......+4-1
= 100+99+98+97...1
= 100*101/2
= 101*50
= 5050

answer Sep 2, 2017 by Salil Agrawal



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