What is the value of 1 1+ 2 + 1 2+ 3 + \cdots + 1 2016+ 2017?

Free Practice Question

PS · Problem Solving

605-655

Roots

What is the value of $\frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + \cdots + \frac{1}{\sqrt{2016}+\sqrt{2017}}$ ?

Correct answer marked below

\sqrt{2016}-1

\sqrt{2017}-1

Correct

\sqrt{2017}

\sqrt{2016}+1

\sqrt{2017}+1

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Comments

AdityaSep 30

The trick here is rationalizing each term, right? Once I did that it telescoped nicely.

Ritik3d ago

Yep, multiply top and bottom by the conjugate of the denominator. Almost everything cancels.

Chiedu4d ago

That's what I missed at first — I tried to combine them directly and got nowhere.

TomásJun 19

Got the telescoping but then second-guessed whether the last term leaves a -1 or a +1. Cost me a minute.

GraciousJun 22

Same, I always write out the first two and last two terms to be safe.

MahdiMay 4

Solid 605-655 level. Not hard once you see the pattern, but the conjugate step isn't obvious under time pressure.

AnshulApr 19

Nice question, took me a bit to spot the rationalization. Thanks for posting!

What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.