# How to find the fractional notation for the given infinite sum below? #0.bar4# = #4/10# + #4/100# + #4/1000# + #4/10000# +.....

The answer is

Let

Then,

Therefore,

By signing up, you agree to our Terms of Service and Privacy Policy

By signing up, you agree to our Terms of Service and Privacy Policy

To find the fractional notation for the given infinite sum (0.\overline{4} = \frac{4}{10} + \frac{4}{100} + \frac{4}{1000} + \frac{4}{10000} + \ldots), we can express it as a geometric series.

Let (S) be the sum of the series:

[S = \frac{4}{10} + \frac{4}{100} + \frac{4}{1000} + \frac{4}{10000} + \ldots]

Multiplying both sides of the equation by 10, we get:

[10S = 4 + \frac{4}{10} + \frac{4}{100} + \frac{4}{1000} + \ldots]

Subtracting the original equation from this, we get:

[10S - S = 4]

[9S = 4]

[S = \frac{4}{9}]

So, the fractional notation for the given infinite sum is (\frac{4}{9}).

By signing up, you agree to our Terms of Service and Privacy Policy

To find the fractional notation for the given infinite sum ( 0.\overline{4} = \frac{4}{10} + \frac{4}{100} + \frac{4}{1000} + \frac{4}{10000} + \ldots ), you can use the concept of geometric series.

First, let's express the infinite sum as a geometric series with common ratio ( \frac{1}{10} ), starting with the first term ( \frac{4}{10} ): [ S = \frac{4}{10} + \frac{4}{10^2} + \frac{4}{10^3} + \frac{4}{10^4} + \ldots ]

Now, we know that the sum of an infinite geometric series with a common ratio ( r ) and first term ( a ) is given by: [ S = \frac{a}{1 - r} ]

In our case, ( a = \frac{4}{10} ) and ( r = \frac{1}{10} ). Substituting these values into the formula, we get: [ S = \frac{\frac{4}{10}}{1 - \frac{1}{10}} ]

Simplifying the denominator: [ S = \frac{\frac{4}{10}}{\frac{9}{10}} ] [ S = \frac{4}{9} ]

Therefore, the fractional notation for the given infinite sum ( 0.\overline{4} ) is ( \frac{4}{9} ).

By signing up, you agree to our Terms of Service and Privacy Policy

- #a# i s The arithmetic mean of two positive numbers #b and c# . #G_1# and #G_2# are the geometric mean between the same positive numbers #b and c# so prove that #G_1^3+G_2^3#=#2abc# ?
- Given an arithmetic progression with a20 =70 and s20=640 find the first term and the common difference ?
- What is the 8th term of the geometric sequence if #a_3 = 108# and #a_5 = 972#?
- What is the sum of the geometric sequence 2, 10, 50, … if there are 8 terms?
- How to answer these using geometric progression formula ?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7