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Math Student

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Method of Differences (Series)

Hi, I'm really stuck on this question. >_< I'm not sure how you re-arrange it to get the answer in the book.

Show that

Show also that

I am able to do the first part, but on the second I get stuck. I get the equation to be

So, where have I gone wrong?

However, when I use either of the methods, I'm not able to get the right answer (ie, actually adding several numbers)

Please help!

Math Student

Guest

Re: Method of Differences (Series)

Math Student

Guest

Re: Method of Differences (Series)

This is so strange!

When I actually do the summation, for example:

1/3 + 1/8 + 1/15 = 21/40

Then n should be 3 in the equation.

However, when you substitute it into their equation, it gives 11/24

Whereas, when you say n = 4, then you DO get 21/40

What is the reason for this? Is there something I've missed?

This does mean that my equation is wrong.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Method of Differences (Series)

n should be 4 in your example. You're probably getting confused because it starts at 2.

Also, you can get from your answer to the book's answer by taking away an extra 1/(n+1).
I'm guessing you must have lost that term somewhere in your workings.

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Why did the vector cross the road?
It wanted to be normal.

Math Student

Guest

Re: Method of Differences (Series)

Okay... so if it does begin at 2, then the number of terms would be 4?

I never knew that.

Does this mean if it begins at three, and I add together 3 terms, starting at 3, then n would be 5?

(And I'll check and see if I can find the missing bit. >_<)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Method of Differences (Series)

Yes, n would be 5 in that example.

The number on top of a summation sign doesn't tell you the amount of terms in the sum, it tells you where r stops.

So,

means f(3) + f(4) + f(5).

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Why did the vector cross the road?
It wanted to be normal.