Math sequences

posted by Lala

Determine the smallest interger n such that 1+(4/5)+(4/5)^2+...+(4/5)^n>4.9
Please explain ti me about thisquestion. I can'tunderstand it.

  1. Reiny

    you have a geometric series with
    a = 1 and r = 4/5

    sum(n) = a(1 - r^n)/(1-r) > 4.9

    1(1 - (4/5)^n)/1/5 > 4.9
    1 - (4/5)^n > .98
    (4/5)^n < .02

    suppose we let .8^n = .02
    log .8^n = log .02
    n = log.02/log.8 = 17.53

    testing:
    if n = 17 , sum(17) = (1 - .8^17)/.2 = 4.8874 < 4.9
    if n = 18 , sum(18) = (1-08^18)/.2 = 4.9099 > 4.9

    So the smallest value of n is 18

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