5. Find the sum: 216 – 36 + 6 – 1…+ 1/7776?

3 Answers

• Use the geometric series formula:

  a + ar + ar^2 + … + ar^n = a(1-r^{n+1})/(1-r).

  In this case, a=216, r=-1/6, and n=8, so the sum is

  216(1-(-1/6)^9)/(1-(-1/6)) = 1439671/7776 = 185.142876

• Hi Allie

  This is a geometric series with a = 216 and r = -1/6

  So a.r^n-1 = 1/7776

  216 (-1/6)^n-1 = 1/7776

  (-1/6)^n-1 = 1/216*7776 = (-1/6)8

  so n-1 = 8

  n=9

  Sum of geometric series = a (1-r^n) / (1-r)

  = 216 (1 – (1/6)^9) / (1 – 1/6)

  = 216 (6^9 – 1) /5*6^8

  = (6^9 – 1) / 5*6^5 = 259.2

• 185.14

  Source(s): Electrical Engineer