Series and sequence-1

Algebra Level 3

The value of ${ 2 }^{ \frac { 1 }{ 4 } }\times{ 4 }^{ \frac { 1 }{ 8 } }\times{ 8 }^{ \frac { 1 }{ 16 } }\times \cdots \times \ldots$ is

(An IITJEE question)

1 4 2 3/2

1 solution

Kandarp Singh
Jun 25, 2014

let it is equal to ${ 2 }^{ s }$ where S= $\frac { 1 }{ 4 } +\frac { 2 }{ 8 } +\frac { 3 }{ 16 } +\frac { 4 }{ 32 } +..................$ and S/2 = $\frac { 1 }{ 8} +\frac { 2 }{ 16 } +\frac { 3 }{ 32 } +\frac { 4 }{ 64 } +..................$ . Subtracting will give S/2= $\frac { 1 }{ 4 } +\frac { 1}{ 8 } +\frac { 1 }{ 16 } +..................$ = $\frac { \frac { 1 }{ 4 } }{ 1-\frac { 1 }{ 2 } } =\frac { 1 }{ 2 }$ =S=1 Hence, given product is $\boxed { { 2 }^{ 1 } }$ = 2

marvellous

ayush khare - 6 years, 11 months ago

the problem seems sOoooo easy but actually it is not s0!

Ashesh Choudhury - 6 years, 11 months ago

exactly the same as I did!!

Kartik Sharma - 6 years, 10 months ago

Series and sequence-1

1 solution

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