Cheenta
How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?
Learn More

TIFR 2013 problem 31 | Inequality problem

Let's discuss a problem from TIFR 2013 Problem 31 based on inequality.

Question: TIFR 2013 problem 31

True/False?

The inequality \( \sqrt{n+1}- \sqrt{n} < \frac{1}{ \sqrt{n} } \) is false for all n such that \( 101 \le n \le 2000 \)

Hint:

Simplify the given inequality

Discussion:

\( \sqrt{n+1}- \sqrt{n} =  \frac {n+1- n}{ \sqrt{n+1}+ \sqrt{n} } \)

\(=  \frac {1}{ \sqrt{n+1}+ \sqrt{n}}  < \frac {1}{ \sqrt{n}} \) This holds for any natural number \(n\).

So the inequality is actually true for all natural numbers.

Useful links:

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

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.
JOIN TRIAL
support@cheenta.com