A statement Sn about the positive integers is given Write st

A statement S_n about the positive integers is given. Write statements S_1, S_2, and S_3, and show that each of these statement is true. S_n: 4 + 9 + 14 +. .. + (5n - 1) = n(5n + 3)/2 Use mathematical induction to prove that the statement is true for every positive integer n 10 + 20 + 30 +. .. + 10n = 5n(n + 1)

Solution

Here we need to find the sum of the infinite series which is:
60 + 60*.6 + 60*.6^2 + 60*.6^3 ...
The sum of an infinite geometric series in the form a + ar + ar^2 + ar^3 ... is a/(1-r).
So, in this case, the sum of the series would be
60/(1-.6)
=60/.4
=150.
So, the pendulum bob will swing a total of 150 inches