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Evaluate the infinite geometric series: 1 + 2/7 + 4/49 + 8/343 + ...

 Nov 4, 2021
 #1
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Evaluate the infinite geometric series: 1 + 2/7 + 4/49 + 8/343 + ...     

 

Well, I see  (2/7)0  +  (2/7)1  +  (2/7)2  +  (2/7)3  +  . . . 

 

but I don't know what to do after that.   

 Nov 5, 2021
 #2
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Hello Guest,

 

Evaluate the infinite geometric series: 1 + 2/7 + 4/49 + 8/343 + ...

 

\({\color{red}Solution:}\)

 

\(1 + \frac{2}{7} + \frac {4}{49} + \frac {8}{343} + \mbox { } ...\)

 

\( \mathcal{ \mbox {Like Guest said it right } } \mbox { } (^2/_7)^0 + (^2/_7)^1 + (^2/_7)^2 + (^2/_7)^3 + \mbox { } ...\)

 

Use the double summation sign \(\sum\) .

 

\(\displaystyle\sum_{n=1}^{\infty} \Bigl( \frac {7}{2} \Bigr)^{1 - n} = \frac {7}{5} = 1.4 \) .

 

\(\mathit{ Straight}\)

 Nov 10, 2021

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