Find the sum:

50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 -1^2

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- April 23rd 2007, 01:51 PMceasar_19134Find the sum:...
Find the sum:

50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 -1^2 - April 23rd 2007, 02:41 PMSoroban
Hello, ceasar_19134!

Quote:

Find the sum: .50² - 49² + 48² - 47² + ... + 2² - 1²

*n*squares is given by: .n(n + 1)(2n + 1)/6

The sum of__all__the squares to 50 is: .(50)(51)(101)/2 .= .42,925

Consider the sum of the__even__squares: .2² + 4² + 6² + ... + 50²

. . = .2²(1² + 2² + 3² + ... + 25²) .= .4·(25)(26)(51)/6 .= .22,100

Hence, the sum of the__odd__squares is: .[all] - [even] .= .42,925 - 22,100 .= .20,825

Therefore: .[even] - [odd] .= .22,100 - 20,825 .= .1275