Simple Summation!

Algebra Level 3

∑ k = 1 99 1 k k + 1 + ( k + 1 ) k = ? \large{\sum_{k=1}^{99} \dfrac{1}{k\sqrt{k+1} + (k+1)\sqrt{k}}} = \ ?


The answer is 0.9.

View wiki
Satyajit Mohanty by Satyajit Mohanty , 24, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Telescoping series

18 Helpful 0 Interesting 0 Brilliant 0 Confused

Right! It Telescopes!

Satyajit Mohanty - 5 years, 9 months ago

just did the same bingo!!!

Varun Tandon - 5 years, 9 months ago

It is a pre-rmo 2014 question (for Mumbai region,India)

Saarthak Marathe - 5 years, 9 months ago

Why you are substituting 1 and 100 in the last line , can you elaborate more please ?

Syed Baqir - 5 years, 9 months ago

Log in to reply

I did a shortcut. Sorry. For k=2 to k=99, the terms will just cancel each other (by pairs). Take note of the (+) and (-). You can expand the summation for several terms to see the pattern.

Vincent Miller Moral - 5 years, 9 months ago

Log in to reply

Thank you very much .

Syed Baqir - 5 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...