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March 30, 2017

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use the method of Gauss to find the sum.

2+4+6+...+300

is it 300(300+2)/2 = 45300

  • math - ,

    close, but incorrect

    there are only 150 terms in the sequence 2,4,6,.. 300

    so according to Gauss, it would be
    150(2+300)/2
    = 22650

    Proof: long way
    a = 2 , d = 2
    t(n) = a+(n-1)d
    300 = 2 + (n-1)2
    300 = 2 + 2n - 2
    n = 150

    S(150) = (150/2)(4 + 149(2))
    = 22650

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