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Let x=3^1/3.3^2/9.3^3/27........∞ then x^1/3 is equal to

Let x=3^1/3.3^2/9.3^3/27........∞ then x^1/3 is equal to

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
first powerof 3 are arranged.
 
S =         1/3 + 2/9 + 3/27 +........
 
S/3 =              1/9 + 2/27 + …....
 
now subtract
 
2S/3 = 1/3 + 1/9 + 1/27 +.......
 
2S/3 = 1/3 / (1- 1/3)
 
2S/3 = ½
 
S = ¾
 
now coming back to question.
 
x = 3^S
 
x = 3^(3/4)
 
hence x^1/3 = 3^1/4

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