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1+1/2+1/3+1/4+1/5 is what?

1+1/2+1/3+1/4+1/5 is what?

If I add the first five reciprocals of natural numbers:

1+1/2+1/3+1/4+1/5

what exactly do I get? Likewise,
what is

1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10 ?

StudyWorks answers both questions in a flash.
8 REPLIES 8
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1+1/2+1/3+1/4+1/5 is what?

Why stop there? What is the value of

1+1/2+1/3+1/4+...+1/97+1/98+1/99+1/100 ?

It seems like a lot of typing would be needed to evaluate this sum. But see the attached StudyWorks file for a shortcut.
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1+1/2+1/3+1/4+1/5 is what?

I am in reply to the second question.
There are ways to evaluate this math problem with simple addition and subtraction.
I will use simple numbers to clarify the solution, but it works with any combination of numbers in series.
lets say we want to add,
1+2+3+4...97+98+99+100
first add the 1+100=101
next add the 2+99=101
next add the3+98=101
see the pattern
how many pairs in 100
50
101*50=5050
try it with a larger problem
say 1+2+3+4...497+498+499+500
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1+1/2+1/3+1/4+1/5 is what?

Back on 6/5/00, in a thread entitled "1+2+3+4+...+100 is what?", the problem of adding lots of consecutive integers was discussed (like you've done).

But adding lots of reciprocals of consecutive integers is much harder. I don't believe that there is any shortcut here.

Bonnie
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1+1/2+1/3+1/4+1/5 is what?

Change everything to a decimal and then add! If you don't know what decimal it is, just divide the top over the bottom.
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1+1/2+1/3+1/4+1/5 is what?

Welcome to the Collab.

While your help is welcomed, any posting more than 1 month old is unlikely to warrent any additional replies, since homework rarely has that much longevity.


TTFN,
Eden
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1+1/2+1/3+1/4+1/5 is what?

For people who want to read this and don't understand addition of number such as 1+2+3+...98+99+100. There is an easy method if you see such numbers are being added.
Firt Multiply the last term to the middle term of the whole terms, which is 100x50 then add the result to the middle term of the whole terms as 100x50+50
100x50=5000
5000+50=5050
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1+1/2+1/3+1/4+1/5 is what?

On 6/29/2003 12:12:10 PM, User04 wrote:
>For people who want to read
>this and don't understand
>addition of number such as
>1+2+3+...98+99+100. There is
>an easy method if you see such
>numbers are being added.
>Firt Multiply the last term to
>the middle term of the whole
>terms, which is 100x50 then
>add the result to the middle
>term of the whole terms as
>100x50+50
>100x50=5000
>5000+50=5050

This is actually discussed in the other thread that you replied to. While your method works for an odd number of terms, it does not deal well with an even number of terms.

TTFN,
Eden
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1+1/2+1/3+1/4+1/5 is what?

wow thx it helps
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