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))