The great Ramanujan limit

Calculus Level 3

$\large \lim_{n \to 0} \dfrac{1}{(\sqrt{n+1}+\sqrt{n})(\sqrt[4]{n+1}+\sqrt[4]{n})\cdots(\sqrt[2^{1729}]{n+1}+\sqrt[2^{1729}]{n})} = \, ?$

1729^{-1}

0

It can't be determined None of these.

1

-1

2^{1729^{-1}}

1 solution

Rishabh Jain
Mar 23, 2016

Simple substitution of $n=0$ gives the answer since we are not getting any indeterminate form. Hence answer= $\Large{\dfrac{1}{\underbrace{1\cdot 1\cdot 1\cdots 1 }_{\color{#D61F06}{\text{1729 times}}}}}\\\huge=\boxed{1}$

That's great! (+1)

Rohit Udaiwal - 5 years, 2 months ago

Truly speaking, I at first sight started to rationalise that stuff only after realising what a fool I am since no such thing is required.... I always love solving your questions... Their originality is amazing... Keep posting good questions... :-)

Rishabh Jain - 5 years, 2 months ago

Yeah you saw my rationolised solution but I realised the same thing.

Rohit Udaiwal - 5 years, 2 months ago

The great Ramanujan limit

1 solution

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