#7 Measure your Calibre

Algebra Level 5

S = 1 + 1 2 + 1 3 + 1 4 + + 1 99 + 1 100 \large S = 1 + \frac 1{\sqrt 2} + \frac 1{\sqrt 3} + \frac 1{\sqrt 4} + \cdots + \frac 1{\sqrt{99}} + \frac 1{\sqrt{100}}

Find S \lfloor S \rfloor .

Notation: \lfloor \cdot \rfloor denotes floor function .


Other problems: Check your Calibre


The answer is 18.

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1 solution

Rajdeep Brahma
Jun 15, 2018

Use induction to prove that k + 1 \sqrt {k+1} - k \sqrt {k} < 1 2 k \frac{1}{2* \sqrt {k}} < k \sqrt {k} - k 1 \sqrt {k-1} ,Then proceed you will easily get the answer by telescoping series. :) .

True. Did the same way !

Md Zuhair - 2 years, 12 months ago

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oh nice :)

rajdeep brahma - 2 years, 12 months ago

try out this 'Lyttelton-Bondi Model for the Expansion of the Universe' inn my post

rajdeep brahma - 2 years, 12 months ago

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Ok sure. And why have you deleted whatsapp? When will you return? How was your JEE Adv?

Md Zuhair - 2 years, 12 months ago

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@Md Zuhair no I will come in wtsapp later will talk then.

rajdeep brahma - 2 years, 12 months ago

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@Rajdeep Brahma Okay .. sure

Md Zuhair - 2 years, 12 months ago

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