Calculus

Write the statements for the basis, the induction hypothesis, and the induction step for the questions below.

1. 1 + 2 +…+n = n(n+1)/2

2. 1/1*2 + 1/2*3+…+1/n*(n+1) = n/n+1

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  1. for k=1, 1 = 1(2)/2
    hyp: as shown
    1+...+ k + (k+1) = k(k+1)/2 + (k+1)
    = [k(k+1) + 2(k+1)]/2
    = (k+1)(k+2)/2

    for k=1, 1/1*2 = 1/2

    1/1*2 + ... + 1/k(k+1) + 1/(k+1)(k+2)
    = k/(k+1) + 1/(k+1)(k+2)
    = (k(k+2) + 1)/(k+1)(k+2)
    = (k+1)^2 / (k+1)(k+2)
    = (k+1)/(k+2)

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