A pendulum bob swings 6.0 cm on its first oscillation. On each subsequent oscillation the bob travels 1/3 of the previous distance. Find the total distance the bob travels before coming to rest.

Answer 1

6 + 6/3 + 6/3^2 + 6/3^3 + ...

we have a GS, where a = 6 and r = 1/3

sum(infinite number of terms) = a/(1-r)
= 6/(1-1/3)
= 6/(2/3)
= 6*3/2 = 9

check:
sum(1) = 6
sum(2) = 6 + (1/3)(6) = 8
sum(3) = 6 + 6/3 + 6/9 = 8 2/3
sum(4) = ....... = 8 8/9
sum(5) = .... 8 26/27
etc