Question

Consider the infinite geometric series 1/2+1/6+1/18+1/54+1/162+ . . .. Find the partial sums Snfor n=1,2,3,4, and 5. Round to the nearest hundredth. Then describe what happens to Sn as n increases. S1=

Answer 1

S5 = 0.75

As n increase, the terms gets smaller and the harder for partial summation to approach whole number.

Explanation:

When the numerical value of r is less than 1 ( - 1 < r < 1), then the formula Sn = a(1−r^n)/(1−r) is used.

Where a = first term

r = common ratio

n = number of terms

So a = 1/2

Second term = 1/6

r = S2/a

r =( 1/6 )/(1/2)

r = 1/3

n = 5

S5 = 1/2(1−(1/3)^5)/(1−(1/3))

S5 = 0.7469

To nearest hundredth

= 0.75

As n increase, the term gets smaller and the harder for the summation to approach 1 .