Sequences and Series

RickyOswaldIOW · 2007-01-30 08:30:44

Write the following series in ∑ notation:

This is a very simple progression but the technique I am using does not seem to yield the right answer, which is:

Here is my method;

Work out the common difference, I subtract the first in the series from the second:

So the difference is 1 -> 1r. Next I go back one term before the start of the series:

Now I add these two terms together for the general term:

As you can see, I've already gone wrong! But I will continue... Find the values of r for the first and last terms:

and:

Now I write down the ∑ notation:

This method works fine for the other questions, where am I going wrong?

Last edited by rickyoswaldiow (2007-01-30 08:31:10)

Zhylliolom · 2007-01-30 08:35:45

Both of the answers give the same sum, they just look different. If you write out your answer term by term you will see that it is correct.

RickyOswaldIOW · 2007-01-30 08:38:27

I see this, is it then that the answer the book suggests is a simplified version of my answer? If so, what is the common method to simplify?

Ricky · 2007-01-30 09:48:02

It's like one person saying, "The answer is 1 + 1" and another saying, "No, you're wrong. The correct answer is 2."

pi man · 2007-01-30 10:09:15

I agree. Your answer differs from the text book because you're using different ranges of r. The text book uses r = 2 to 10 and you use r = 1 to 9. The following would also be a valid (and equal) answer:

RickyOswaldIOW · 2007-01-30 11:28:18

So they'd definately accept my answer? What I don't understand is - why would they teach me this method that I use on all of their questions, then put the answer in a different format?! It's a crazy world we live in :S

mathsyperson · 2007-01-30 11:35:02

They've just simplified it a bit. Instead of having the summation term involving a power of r+1, they've just changed the sum boundaries so that it can be in terms of r instead.

Just like saying that 3/7 * 5/6 = 15/42, but then simplifying it to give 5/14 instead.

RickyOswaldIOW · 2007-01-31 00:47:37

I think I should have made a change in this step:
I've equated

as

Which is just

Math Is Fun Forum

#1 2007-01-30 08:30:44

Sequences and Series

#2 2007-01-30 08:35:45

Re: Sequences and Series

#3 2007-01-30 08:38:27

Re: Sequences and Series

#4 2007-01-30 09:48:02

Re: Sequences and Series

#5 2007-01-30 10:09:15

Re: Sequences and Series

#6 2007-01-30 11:28:18

Re: Sequences and Series

#7 2007-01-30 11:35:02

Re: Sequences and Series

#8 2007-01-31 00:47:37

Re: Sequences and Series

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