Sum of the Series

Calculus Level 3

s = 1 2 + 1 3 + 1 4 + . . . + 1 10000 s= \frac 1{\sqrt 2} +\frac 1{\sqrt 3} + \frac 1{\sqrt 4} +... +\frac 1{\sqrt {10000}}

Find ⌊ s ⌋ \lfloor s \rfloor .


The answer is 197.

Adharsh M by Adharsh M , 20, India

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1 solution

Adharsh M
Jun 13, 2017

integral 1/root x with limits 2 to 10000 will give you value 197.18....... use Greatest integer function to get answer.

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Is your answer an underestimate or an overestimate?

How can we guarantee that the given expression will be 197.xx, as opposed to say 196.98?

Calvin Lin Staff - 3 years, 12 months ago

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there is an inequality I guess

Adharsh M - 3 years, 12 months ago

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Please be courteous in your replies. If you are sure of your answer, you should be able to completely prove it in your solution. It is rather lacking, as it is missing a thorough explanation. Why did you use an integral? How did you know to use an integral? Why does an integral only approximate this sum, and does it underestimate or overestimate it?

Zach Abueg - 3 years, 12 months ago

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@Zach Abueg – Apology . If you have the correct explanation, please provide , however the answer is 197.

Adharsh M - 3 years, 12 months ago

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