Consider the following repeating decimal. 0.819 (a) Write the repeating decimal as a geometric series. 0.819...

Question

Question

Answer 1

Answer #1

$0.8\overline{19}$

(a) $0.8\overline{19}$ = 0.819191919...... = 0.8+0.019+0.00019+0.0000019+......

= 0.8+ 0.019 + 0.019x(0.01)+0.019x(0.01)2+........

0.819 = 0.8 +Σο.019(0.01) n=0

(b) Sum of geometric series with infinite number of terms and common ratio less than1 = a/(1-r)

Sum = 0.8+0.019/(1-0.01) = 4/5+19/990 = 811/990

Answer 2

Similar Homework Help Questions

For part A please show it clearly make the Box Consider the following repeating decimal. 0.819...

For part A please show it clearly make the Box Consider the following repeating decimal. 0.819 (a) Write the repeating decimal as a geometric series. 0.815 = 0.819 0.819 = 0.819 x + [ 0.00019 0.00019 x ( 10-2 10^-2 ) n = 0 (b) Write the sum of the series as the ratio of two integers. 811/990 Need Help? Read It Talk to a Tutor
3. (a) Write the repeating decimal as a geometric series and (b) write the sum of...

3. (a) Write the repeating decimal as a geometric series and (b) write the sum of the series as the ratio of two integers. 0.080808080808... = 0.08
hey thanks :0 Express the repeating decimal 0.123 as a geometric series and then use the...

hey thanks :0 Express the repeating decimal 0.123 as a geometric series and then use the sum of that series to express the decimal as the ration of two integers.

Find the sum of the finite geometric series. 31 n=1 Need Help? Read It Watch It...

Find the sum of the finite geometric series. 31 n=1 Need Help? Read It Watch It Talk to a Tutor 11. [-/1 Points] DETAILS Find the sum of the finite geometric series. 21 n-1 Need Help? Read it Talk to a Tutor 12. (-/1 Points] DETAILS Find the sum of the finite geometric series. er n-1 Write the rational number as the quotient of two integers in simplest form. 0.7 Need Help? Read It Watch It Talk to a Tutor...
18) Write 0.2121 as a fraction of two integers using a geometric series 19) Evaluate the...

18) Write 0.2121 as a fraction of two integers using a geometric series 19) Evaluate the improper integral; } dos
4) Evaluate dx (4 – x²) 3/2 5) Evaluate the improper integral ſxe**dx 0 6) Express...

4) Evaluate dx (4 – x²) 3/2 5) Evaluate the improper integral ſxe**dx 0 6) Express the repeating decimal 0.123 as a geometric series and then use the sum of that series to express the decimal as the ration of two integers.

Can u please explain the steps? thanks SO much! There are three different parts. 4(:)n 1 consider the infinite geometric series Σ -1 In this image, the lower limit of the summation notation is &#...

Can u please explain the steps? thanks SO much! There are three different parts. 4(:)n 1 consider the infinite geometric series Σ -1 In this image, the lower limit of the summation notation is "n 1". a. Write the first four terms of the series b. Does the series diverge or converge? c. If the series has a sum, find the sum. 4(:)n 1 consider the infinite geometric series Σ -1 In this image, the lower limit of the summation...
express the repeating decimal as a quotient of two integers 1.63

express the repeating decimal as a quotient of two integers1.63
Problem 1 Geometric Series. We will need to sum the geometric series to simplify some of...

Problem 1 Geometric Series. We will need to sum the geometric series to simplify some of the partition functions developed in class. Prove that the geometric series 7:0 for r| < 1. You may find it helpful to consider the partial sums Sj ?, xk 1+1+-.+4 and rSi =x+x2 + +z?+1 take the limit J ? 00, Can you see why the geomet ric series converges for r < 1 and diverges for ll 2 1 Explain. . You will...

12-1 + + 4. The series £9) .. is a geometric series. 4 n=1 Which of...

12-1 + + 4. The series £9) .. is a geometric series. 4 n=1 Which of the following is true? (a) The series is convergent and its sum is less than 1/2. (b) The series is convergent and its sum is 1/2. (c) The series is convergent and its sum is 2/3. (d) The series is convergent and its sum is more than 2/3. IS 5. For positive numbers a and r, it is known that the geometric series divergent....