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Chapter 1: Q3P (page 1)

Use equation (1.8) to find the fractions that are equivalent to the following repeating decimals:

0.55555...

Short Answer

Expert verified

The equivalent fraction for0.55555... is 59.

Step by step solution

01

Explanation of solution

Given number is 0.55555....

The expression for sum of infinite GP series is S=a1-r.

Where, S is the sum of GP up to infinite terms.

02

Equivalent fraction

Fractions having the same numerator and denominator but different numerators and denominators are called equivalent fractions.

03

Calculation

An example of how to write the number is as follows:

0.55555...=0.5+0.05+0.005+0.0005+....+0.5110n

The words will create GP with a=0.5and r=1/10.

Substitute 0.5 for a and 1/10 for r in above equation.

S=0.51-110=510910=59

Hence, the fraction is 59.

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Most popular questions from this chapter

In the following problems, find the limit of the given sequence as

n鈫�鈭�

Estimate the Error if鈭�n=1鈭�xnn3is approximated by the sum of its first three terms for|x|<12.

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Method2:Incosx=-鈭�0xtanuduUse the series of Example 2 in method B.

鈭�0xsintdtt

Derive the formula (1.4) for the sum Snof the geometric progression Sn=a+ar+ar2+.....arn-1.Hint: Multiply Snby rand subtract the result fromSn; then solve for Sn. Show that the geometric series (1.6) converges if and only if r<1; also show that if r<1, the sum is given by equation (1.8).
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