Calculator Killer 6

Algebra Level 2

$\large 100^2 - 99^2 + 98^2 - 97^2 + \cdots +2^2 - 1^2 = \, ?$

5050 50 10100 10000

2 solutions

Akshat Sharda
Dec 17, 2015

We know ,

$a^2-b^2=(a+b)(a-b)$

$100^2 - 99^2 + 98^2 - 97^2 +\ldots +2^2 - 1^2 \\ (100+99)(100-99)+(98+97)(98-97)+\ldots(2+1)(2-1) \\ 100+99+98+97+\ldots+2+1=\frac{100\times101}{2}=\boxed{5050}$

Moderator note:

Great approach to this problem.

Excellent! Great shortcuts. :)

Zandra Vinegar Staff - 5 years, 6 months ago

Siva Prasad
Dec 17, 2015

I have already shared the same question in negative form to brilliant..! :)

Calculator Killer 6

2 solutions

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