lim_(n→∞) (1(2(3(4(5(6(....(n.)^(1/2) ..)^(1/2) )^(1/2) )^(1/2) )^(1/2) )^(1/2) )^(1/2) =?


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Question Number 99793 by bachamohamed last updated on 23/Jun/20

$l i \underset{n \to \infty}{m} (1 {(2 {(3 {(4 {(5 {(6 {(. . . . {(n .)}^{\frac{1}{2}} . .)}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}})}^{\frac{1}{2}} = ?$
Commented by Dwaipayan Shikari last updated on 23/Jun/20

$\sqrt{1 \sqrt{6}}$
Commented by bachamohamed last updated on 23/Jun/20

$b u t$ $3 = \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + 4 \sqrt{1 + 5 \sqrt{. . . . .}}}}} = \sqrt{1 + (2 \sqrt{1 + (3 \sqrt{1 + (\sqrt{1 + (4 \sqrt{. . . . .)})})}))}) . . .})$ $3 \neq \sqrt{3 \sqrt{4 \sqrt{5 \sqrt{6 \sqrt{7 . . . .}}}}}$
Commented by Dwaipayan Shikari last updated on 23/Jun/20

$I h a v e c o m e t o k n o w t h a t m y p r o c e s s i s w r o n g . I a m t r y i n g a n o t h e r m e t h o d$
Commented by Dwaipayan Shikari last updated on 23/Jun/20

$G r e a t q u e s t i o n . A l t h o u g h s i r i a m a s t u d e n t$
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