Question

the sum upto the infinity of the series 4/7-5/49+4/343+.......is
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

f(x) = $\frac{4}{7} - \frac{5}{49} + \frac{4}{343} - . . . .$

To find,

Sum of f(x) unto infinity.

Solution,

The sum of the function f(x) up to infinity is $\frac{23}{48}$.

We can simply solve the mathematical problem by the following process.

It is given that,

f(x) = $\frac{4}{7} - \frac{5}{49} + \frac{4}{343} - . . . .$

     = $\frac{4}{7} - \frac{5}{7^2} + \frac{4}{7^3} - . . . .$

     = $(\frac{4}{7}+\frac{4}{7^3} + \frac{4}{7^5} ...) - (\frac{5}{7^2} + \frac{5}{7^4}+...)$

     = $4( \frac{1}{7} + \frac{1}{7^3}+..) - 5( \frac{1}{7^2}+\frac{1}{7^4} +...)$

     = $4 ( \frac{\frac{1}{7} }{1-(\frac{1}{7})^2 } )-5 (\frac{(\frac{1}{7})^2 }{1 - (\frac{1}{7})^2 } )$

     = $4 (\frac{7}{48} )-5(\frac{1}{48} )$

     = $\frac{28}{48}-\frac{5}{48}$

     = $\frac{23}{48}$

Thus, the sum of the function f(x) up to infinity is $\frac{23}{48}$.