Squares minus squares

Algebra Level 2

10 0 2 − 9 9 2 + 9 8 2 − 9 7 2 + … + 6 2 − 5 2 + 4 2 − 3 2 + 2 2 − 1 2 = ? 100^2-99^2+98^2-97^2+\ldots+6^2-5^2+4^2-3^2+2^2-1^2= \ ?

23024 50005000 10000 5050

Kartik Sharma by Kartik Sharma , 20, India

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1 solution

Kartik Sharma
Jun 22, 2015

100²-99²+98²-97²......+2²-1² (100+99)(100-99)+(98+97)(98-97).....+(2+1)(2-1) =100+99+98....+3+2+1=5050

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks,nice soln

Akhil Bansal - 5 years, 11 months ago

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