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Math Help - Find the sum:...

  1. #1
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    Find the sum:...

    Find the sum:
    50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 -1^2
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  2. #2
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    Hello, ceasar_19134!

    Find the sum: .50 - 49 + 48 - 47 + ... + 2 - 1
    The sum of the first 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: .2 + 4 + 6 + ... + 50

    . . = .2(1 + 2 + 3 + ... + 25) .= .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

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