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Chapter 12: Q 2. (page 824)

If r<1, the sum of the geometric series a

鈭�k=1鈭�ark-1is ________ .

Short Answer

Expert verified

Ifr<1, the sum of the geometric series a 鈭�k=1鈭�ark-1is a1(1-r).

Step by step solution

01

Step 1. Given information.

If r<1, the sum of the geometric series a 鈭�k=1鈭�ark-1is _________.

  • A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
02

Step 2. Fill in the blanks.

The sum snof first nterms of a geometric sequence is given by

sn=a1(1-rn)(1-r)sn=a1(1-r)-a1rn)(1-r)

If r<1then rnapproaches 0asn鈫�鈭�then the terma1rn(1-r)approaches 0and snapproaches a1(1-r)as n鈫�鈭�.

Therefore, ifr<1the sum of the geometric series a鈭�k=1鈭�ark-1isa1(1-r).

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Most popular questions from this chapter

In Problems 71-82, find the sum of each sequence.

鈭�k=140k

Find x so that x, x + 2, and x + 3 are consecutive terms of a geometric sequence.

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

1+13+19+.....

In Problems 11鈥�16, evaluate each factorial expression.

12!10!

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

6+2+23+.....
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