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Chapter 12: Q 47. (page 825)

For Problems 45鈥�50, use a graphing utility to find the sum of each geometric sequence.

鈭�n=11523n

Short Answer

Expert verified

The sum of the given sequence is1.9954

Step by step solution

01

Step 1. Write the given information.

The given sequence is 鈭�n=11523n

02

Step 2. Find the common ratio.

a1=23,a2=232a2a1=23223=23r=23

03

Step 3. Find the sum.

The formula for the sum of nth term is sn=a1(1-rn)1-r

s15=23路1-23151-23=23路1-231513=2路1-2315=1.9954

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Most popular questions from this chapter

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

2+43+89+....

In Problems 17鈥�28, write down the first five terms of each sequence.

bn=2n+12n

In Problems 61鈥�70, express each sum using summation notation.

1+3+5+7+....+212-1

In Problems 61鈥�70, express each sum using summation notation.

3+322+333+.....+3nn

Growth of a Rabbit Colony:

A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months?

[Hint: The Fibonacci sequence models this colony. Do you see why?]
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