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March 25, 2017

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Which of the following sums is larger and by how much? (n=1)

Y1 = 7 over Σ 15/4(pi/10)^n

Y2= 11 over Σ 17/4(4/13)^n

  • MATH - ,

    did you mean
    Σ ((15/4) (π/10)^n , where n goes from 1 to 7 ?

    of so, then you would have

    (15/4) [ π/10 + π^2/100 + ... + π^7/10^7)
    the [..] is a geometric series where a=π/10 and r = π/10 for 7 terms

    the value of the [..]
    = (π/10)((π/10)^7 - 1)/(π/10 - 1) = appr. .4579
    so
    Σ ((15/4) (π/10)^n , where n goes from 1 to 7
    = (15/4)(.4579) = 1.717

    evaluate the second part the same way, and compare sums

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