GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 08:44

### 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

# The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Feb 2011
Posts: 108
The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

10 Jul 2011, 07:40
1
3
00:00

Difficulty:

75% (hard)

Question Stats:

34% (01:44) correct 66% (01:27) wrong based on 88 sessions

### HideShow timer Statistics

The value of $$\frac{1}{2} + (\frac{1}{2})^2 + (\frac{1}{2})^3 + ... + (\frac{1}{2})^{20}$$ is between?

A. $$\frac{1}{2}$$ and $$\frac{2}{3}$$
B. $$\frac{2}{3}$$ and $$\frac{3}{4}$$
C. $$\frac{3}{4}$$ and $$\frac{9}{10}$$
D. $$\frac{9}{10}$$ and $$\frac{10}{9}$$
E. $$\frac{10}{9}$$ and $$\frac{3}{2}$$

M17-05

_________________
target:-810 out of 800!
Retired Moderator
Joined: 16 Nov 2010
Posts: 1260
Location: United States (IN)
Concentration: Strategy, Technology
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

10 Jul 2011, 07:44
This is a GP

So the sum is:

1/2(1 - (1/2)^19)/(1 - 1/2)

= 1 - (1/2)^19

Clearly this is > 9/10 (because (1/2)^19 is a very small number) and < 10/9 or 1

So D is the best choice
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Current Student
Joined: 26 May 2005
Posts: 457
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

10 Jul 2011, 07:47
AnkitK wrote:
What is 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 between?
A.1/2 and 2/3
B.2/3 and 3/4
C.3/4 and 9/10
D.9/10 and 10/9
E.10/9 and 3/2

What is shortest approach for this question?

the shortest way wud be t solve first 4/5 fraction
1/2 = 0.5
1/4 = 0.25
1/8 = 0.125
1/16 =.0625
1/32 = 0.03125
values after these becomes very small....

A,B ,C,E fails
only D is correct

PS: u can infact leave after 1/16... total = .93
Manager
Joined: 28 Jul 2011
Posts: 81
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

02 Nov 2011, 07:48
Pretty hard to solve under 2 mins. Should be D.
Manager
Joined: 29 Oct 2011
Posts: 143
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

02 Nov 2011, 08:27
Unless you know the sum formula for the geometric sequence, using sudhir18n's method would be easiest.
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

23 Jan 2015, 09:58
[quote="AnkitK"]What is 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 between?
A.1/2 and 2/3
B.2/3 and 3/4
C.3/4 and 9/10
D.9/10 and 10/9
E.10/9 and 3/2

How can solve this guestion under 2 mins.
_________________
Click +1 Kudos if my post helped
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

23 Jan 2015, 09:59
AnkitK wrote:
What is 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 between?
A.1/2 and 2/3
B.2/3 and 3/4
C.3/4 and 9/10
D.9/10 and 10/9
E.10/9 and 3/2

What is shortest approach for this question?

How can solve this guestion under 2 mins
_________________
Click +1 Kudos if my post helped
Math Expert
Joined: 02 Sep 2009
Posts: 58316
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

23 Jan 2015, 11:21
AnkitK wrote:
The value of $$\frac{1}{2} + (\frac{1}{2})^2 + (\frac{1}{2})^3 + ... + (\frac{1}{2})^{20}$$ is between?

A. $$\frac{1}{2}$$ and $$\frac{2}{3}$$
B. $$\frac{2}{3}$$ and $$\frac{3}{4}$$
C. $$\frac{3}{4}$$ and $$\frac{9}{10}$$
D. $$\frac{9}{10}$$ and $$\frac{10}{9}$$
E. $$\frac{10}{9}$$ and $$\frac{3}{2}$$

M17-05

We have the sum of a geometric progression with the first term equal to $$\frac{1}{2}$$ and the common ratio also equal to $$\frac{1}{2}$$.

Now, the sum of infinite geometric progression with common ratio $$|r| \lt 1$$, is $$sum=\frac{b}{1-r}$$, where $$b$$ is the first term. So, if we had infinite geometric progression instead of just 20 terms then its sum would be $$Sum=\frac{\frac{1}{2}}{1-\frac{1}{2}}=1$$. Which means that the sum of this sequence will never exceed 1. Also since we have a large enough number of terms (20), the sum will be very close to 1, so we can safely choose answer choice D.

One can also use direct formula.

We have geometric progression with $$b=\frac{1}{2}$$, $$r=\frac{1}{2}$$ and $$n=20$$;

$$S_n=\frac{b(1-r^n)}{(1-r)}$$, so:

$$S_{20}=\frac{\frac{1}{2}(1-\frac{1}{2^{20}})}{(1-\frac{1}{2})}=1-\frac{1}{2^{20}}$$. Since $$\frac{1}{2^{20}}$$ is very small number then $$1-\frac{1}{2^{20}}$$ will be less than 1 but very close to it.

_________________
Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

23 Jan 2015, 11:32
Tank you so much Bunuel
_________________
Click +1 Kudos if my post helped
Non-Human User
Joined: 09 Sep 2013
Posts: 13136
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?  [#permalink]

### Show Tags

16 Jan 2019, 14:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The value of 1/2 +(1/2)^2 + (1/2)^3.....+(1/2)^20 is between?   [#permalink] 16 Jan 2019, 14:38
Display posts from previous: Sort by