Question

Find the value of 51/2 × 51/4 × 51/8 ....... upto infinity.Find the value of 51/2 × 51/4 × 51/8 ....... upto infinity.​

Answer 1

5^(1/2) * 5^(1/4)  * 5^(1/8)  *............................. = 1

Step-by-step explanation:

Correct Question is

Find Value of 5^(1/2) * 5^(1/4)  * 5^(1/8)  *.............................

= 5 ^(1/2 + 1/4  + 1/8  + .............................................)

This is an GP in power or 5

a = 1/2

r = 1/2

Sum of infinite series GP  = a/(1 - r)

= (1/2)/(1 - 1/2)

= (1/2)/(1/2)

= 1

5^1  = 5

5^(1/2) * 5^(1/4)  * 5^(1/8)  *............................. = 1

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