Sum-it-up!

Calculus Level 3

a n = ∑ i = 1 n 2 − 1 n + i ∑ i = 1 n 2 − 1 n − i a_n = \dfrac{\displaystyle \sum_{i=1}^{n^2-1} \sqrt{n + \sqrt i }}{\displaystyle \sum_{i=1}^{n^2-1} \sqrt{n - \sqrt i } }

Find the value of a_{2019} .

PART ONE


The answer is 2.414.

Kartik Sharma by Kartik Sharma , 19, India

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1 solution

Kartik Sharma
Jun 24, 2019

Since the answer does not depend on the value of n , thus, the value of a_{2019} is nothing but 1+ sqrt(2).

0 Helpful 0 Interesting 1 Brilliant 0 Confused

Great solution!

Chris Lewis - 1 year, 11 months ago

Thanks man !!

Kartik Sharma - 1 year, 11 months ago

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