Finding the Smallest Integer!

Algebra Level 5

1 − ∑ k = 1 n k k ! ( k + 1 + k + 1 ) ≤ 1 12 5 \large{ 1 - \sum_{k=1}^{n} \frac{k}{\sqrt{k!}(k+1+\sqrt{k+1})} \leq \frac{1}{12\sqrt{5}}}

Find the smallest integer n \large{n} which satisfies the above inequality.


The answer is 5.

Satyajit Mohanty by Satyajit Mohanty , 24, India

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1 solution

Satyajit Mohanty
Jul 17, 2015

And therefore the smallest integer n = 5 n = \boxed{5}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Same method here. Did you type all of that using MS Word?

Vishwak Srinivasan - 5 years, 11 months ago

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Well, you can see my other solutions as well. I prefer MS Word in solutions in case of complicated LaTeX.

Satyajit Mohanty - 5 years, 11 months ago

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