 It is currently 26 Jun 2019, 01:47 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. In the sequence al, a2, a3, • • • , aim the kthterm is defin  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Founder  Joined: 18 Apr 2015
Posts: 7019
Followers: 117

Kudos [?]: 1369  , given: 6383

In the sequence al, a2, a3, • • • , aim the kthterm is defin [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 89% (01:15) correct 10% (01:59) wrong based on 19 sessions

In the sequence $$a_1$$, $$a_2$$, $$a_3$$, • • • ,$$a_{100}$$, the $$k_{th}$$ term is defined by $$a_k = \frac{1}{k} - \frac{1}{k+1}$$ for all integers $$k$$ from 1 through 100. What is the sum of the 100 terms of this sequence?

A) $$\frac{1}{10,100}$$

B) $$\frac{1}{101}$$

C) $$\frac{1}{100}$$

D) $$\frac{100}{101}$$

E) $$1$$
[Reveal] Spoiler: OA

_________________ GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 120

Kudos [?]: 1910  , given: 397

Re: In the sequence al, a2, a3, • • • , aim the kthterm is defin [#permalink]
3
KUDOS
Expert's post
Explanation

Remember, the key to most GRE sequence questions is discovering a pattern among the terms. So start off by finding the first few terms and looking for a pattern.

$$a1 = 1 -\frac{1}{1+1}= 1-\frac{1}{2}$$.
$$a2 = \frac{1}{2} -\frac{1}{2+1}= \frac{1}{2} - \frac{1}{3}$$.
$$a3 = \frac{1}{3} -\frac{1}{3+1}= \frac{1}{3} - \frac{1}{4}$$.

Hence sum $$a1 + a2 + a3 ....... = 1-\frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ......$$

So alternate terms terms cancel out. So

$$a100 = \frac{1}{100} - \frac{1}{101}$$

So $$a1 + a2 + a3 ...... a100$$=$$1 - \frac{1}{101} = \frac{100}{101}$$.

Hence option D is correct.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Re: In the sequence al, a2, a3, • • • , aim the kthterm is defin   [#permalink] 11 Mar 2017, 20:57
Display posts from previous: Sort by

In the sequence al, a2, a3, • • • , aim the kthterm is defin  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.