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Calculus

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Use mathematical induction to prove that the statement holds for all positive integers. Also, label the basis, hypothesis, and induction step.


1 + 5 + 9 + … + (4n -3)= n(2n-1)

  • Calculus -

    for k=1: 1 = 1(2-1)
    assume for k
    for n=k+1,

    1+5+...+(4k-3)+(4(k+1)-3) = k(2k-1) + (4(k+1)-3)
    = k(2k-1) + (4k+1)
    = 2k^2 - k + 4k + 1
    = 2k^2 + 3k + 1
    = (k+1)(2k+1)
    = (k+1)(2(k+1)-1)

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