IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q10

Algebra Level 2

$f(n)=\frac{1}{1+\sqrt2}+\frac{1}{\sqrt2+\sqrt3}+\frac{1}{\sqrt3+2}+...+\frac{1}{\sqrt{n-1}+\sqrt{n}}$

For $f(n)$ as defined above, which of the following options are correct?

A: $f(10)=2$
B: $f(15)=3$
C: $f(20)=4$
D: $f(25)=5$

Enter your answer as a 4-digit string of 1s and 9s $-$ 1 for correct option, 9 for wrong. For example: if A and B are correct, and C and D are incorrect, enter 1199. None, one or all may also be correct.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.