How Cheenta works to ensure student success?
Explore the Back-Story

Greatest Integer | PRMO 2019 | Question 22

Join Trial or Access Free Resources

Try this beautiful problem from the Pre-RMO, 2019 based on Greatest Integer.

Greatest integer - PRMO 2019

Find the greatest integer not exceeding the sum \(\sum_{n=1}^{1599}\frac{1}{\sqrt{n}}\)

  • is 107
  • is 78
  • is 840
  • cannot be determined from the given information

Key Concepts

Largest integer



Check the Answer

Answer: is 78.

PRMO, 2019, Question 22

Elementary Number Theory by David Burton

Try with Hints

\(\int\limits_1^{1600}\frac{1}{x}{d}x < \sum_{x=1}^{1599}\frac{1}{\sqrt{n}}\)

\(< 1+\sum_{n=1}^{1599}\frac{1}{\sqrt{x}}{d}x\)

or, \([2\sqrt{x}]_{1}^{1600}< \sum_{n=1}^{1599}\frac{1}{\sqrt{n}}\)

\(< 1+|2{\sqrt{x}}|_1^{1599}\)

or, 78<\(\sum_{n=1}^{1599}\frac{1}{\sqrt{n}} <2\sqrt{1599}-1\)

or, 78 < \(\sum_{n=1}^{1599}\frac{1}{\sqrt{n}}\)<78.97


Subscribe to Cheenta at Youtube

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
Math Olympiad Program