Question Number 100482 by Dwaipayan Shikari last updated on 26/Jun/20

(√(1(√(2(√(3(√(4(√(5(√(6(√7))))))))))))).....∞=???????

Answered by floor(10²Eta[1]) last updated on 27/Jun/20

(√(√(1.2(√(3(√(4(√(5(√(6(√(7...(√n))))))))))))))  (√(√(√(1.2^2 .3(√(4(√(5(√(6(√(7...(√n)))))))))))))  (√(√(√(√(1.2^2 .3^2 .4(√(5(√(6(√(7...(√n))))))))))))  ...=^2^n  (√(1.2^2 .3^2 ...(n−1)^2 n))  =^2^n  (√(n!(n−1)!))  when you take the limit as n  approaches infinite the result is 1  (wolfram alpha)

Commented bybachamohamed last updated on 27/Jun/20

this solution is not correct because  there is an error because   (√(1(√(2(√(3(√(4(√(5(√(.....))))))))))))≠^2^n  (√(1^2 .2^2 .3^2 ..(n−1)^2 n^2 ))  but   (√(1(√(2(√(3(√(...∞))))))))=^2^n  (√(1^2^(n−1)  .2^2^(n−2)  .3^2^(n−3)  ....(n−1)^2^  .n))