MYTUTOR SUBJECT ANSWERS

1095 views

What is the sum of the series 2/3 − 2/9 + 2/27 − ....? (PAT Q1 2013)

This is the sum of a geometric series with an infinite number of terms.

First, find the common ratio:

(-2/9)/(2/3) = -1/3 , (2/27)/(-2/9) = -1/3

Therefore, the common ratio is -1/3

-1<(-1/3)<1 therefore the series will converge to a finite number. 

The general formula for a sum of an infinite geometric series is a/(1-r) where a is the first number in the sequence and r is the common ratio.

So, substituting in the numbers, the sum of the series = (2/3)/(1-[-1/3]) = 1/2

Kirill M. A Level Maths tutor, A Level Further Mathematics  tutor, A ...

2 years ago

Answered by Kirill, an Uni Admissions Test .PAT. tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

9 SUBJECT SPECIALISTS

George S. GCSE Further Mathematics  tutor, A Level Further Mathematic...
£25 /hr

George S.

Degree: Physics (Masters) - Birmingham University

Subjects offered:.PAT., Physics+ 2 more

.PAT.
Physics
Maths
Further Mathematics

“About Me: I am just entering my first year to study Physics at University of Birmingham, I've always enjoyed anything maths based hence my A-level choices, I hope I can help you through your work whether it's GCSE or A-level and maybe...”

£30 /hr

Alex S.

Degree: Physics (Bachelors) - Oxford, St Peter's College University

Subjects offered:.PAT., Physics+ 2 more

.PAT.
Physics
Maths
Further Mathematics

“Studying Physics at the University of Oxford. Looking to tutor maths and physics at all levels, be sure to send me a message if you have any questions!”

£25 /hr

Ana S.

Degree: Physics (Bachelors) - Oxford, Balliol College University

Subjects offered:.PAT., Physics+ 3 more

.PAT.
Physics
Maths
.STEP.
-Oxbridge Preparation-

“A friendly and understanding tutor with three years experience in school clubs, summer camps and private tutoring.”

About the author

£26 /hr

Kirill M.

Degree: Physics (Masters) - Oxford, St Catherine's College University

Subjects offered:.PAT., Physics+ 2 more

.PAT.
Physics
Maths
Further Mathematics

“Me Hi, I'm Kirill, I'm a 3rd year physicist at Oxford. Whether you are looking for exam preparation or for a better understanding of the material that you are covering in your studies of Maths or Physics, I can help you reach your goa...”

You may also like...

Posts by Kirill

What is the sum of the series 2/3 − 2/9 + 2/27 − ....? (PAT Q1 2013)

A car is travelling at 10m/s when it brakes and decelerates at 2ms^-2 to a stop. How long does the car take to stop?

Integrate cos(4x)sin(x)

Other Uni Admissions Test .PAT. questions

How do I evaluate something like 3070^2-3069^2?

How are you to find 2007^2 − 2006^2 without a calculator?

What is the sum of the series 2/3 − 2/9 + 2/27 − ....? (PAT Q1 2013)

How do I approximate an irrational square root without using a calculator?

View Uni Admissions Test .PAT. tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok