# Sum of an Infinite Series

• Apr 11th 2006, 08:45 PM
delpin
Sum of an Infinite Series
A question about "correctness"

Given a question that asks the student to find the sum to infinity of a recurring decimal and the answer is 5.3(repeater) would you be happy to accept 5.3 repeater or would you prefer to see 16/6 or 51/3?

:)
• Apr 11th 2006, 09:56 PM
Bahama.Llama
Can't go wrong with the fraction. The 5.3 is an approximation, the fraction is exact. I prefer to be as exact as possible :)
• Apr 11th 2006, 10:59 PM
delpin
Am I being pedantic?
I have marked the decimal as wrong since I consider it to be an approximation to an infinite number of decimal places Whereas the fraction is exact! I am the odd one out in the staff room.
• Apr 11th 2006, 11:41 PM
TD!
Neither 16/6 (= 2.6...) nor 51/3 (= 17) give the other answer, perhaps you meant 16/3 or they were just other examples.

Of course, 16/3 is exact, but so is 5.3... (where the dots effectively denote an infinite decimal expansion), also noted $\displaystyle 5.\bar 3$. If you just write a finite number of decimals such as 5.3 of 5.333, the anwer is an approximation.

I would prefer 16/3, but if the student makes clear that he means an infinite recurring decimal, the answer is not wrong and should not be marked wrong (imho), unless it was explicitly said (by the teacher, in class of before the test) that a fractional answer was the preferred form.
• Apr 11th 2006, 11:52 PM
delpin
I take your point but...
is 5.3 repeater a sum to infinity?
• Apr 12th 2006, 12:42 AM
TD!
It's not a sum, it's a number and it's exactly equal to 16/3.

You can consider it as the infinite sum:
5 + 0.3 + 0.03 + 0.003 + 0.0003 + ...
• Apr 12th 2006, 09:50 AM
ThePerfectHacker
The thing about infinite decimal expansions is that we define there value to be the limit of the sum.
• Apr 13th 2006, 03:15 AM
topsquark
Quote:

Originally Posted by ThePerfectHacker
The thing about infinite decimal expansions is that we define there value to be the limit of the sum.

Just a quick comment to prove that I have a psychological need to be contrary...

The preceeding comments go for Math. In Physics, don't try to give either a repeating decimal answer or a fraction. The whole significant digits thing really doesn't work well for fractional answers. For example: 17/3 = 6 because 3 only has one significant digit.

One of my favorite songs is to sing "100 Bottles of Beer on the Wall" to the correct number of sig figs! :D (Hint to the joke: 100 - 1 = 100.)

-Dan

Okay! Okay! So I'm a dork! :)
• Apr 15th 2006, 05:23 PM
ThePerfectHacker
Quote:

Originally Posted by topsquark
Just a quick comment to prove that I have a psychological need to be contrary...

:D

Quote:

Originally Posted by topsquark
One of my favorite songs is to sing "100 Bottles of Beer on the Wall" to the correct number of sig figs! :D (Hint to the joke: 100 - 1 = 100.)

The mathematics version goes like this.

"Aleph-Null bottles of beer on the wall,
Aleph-Null bottles of beer,
Pass one around and drink it down,
Aleph-Nulls bottles of bear on the wall.

Aleph...."