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06-12-2000
03:00 AM

06-12-2000
03:00 AM

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.

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.

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8 REPLIES 8

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06-12-2000
03:00 AM

06-12-2000
03:00 AM

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.

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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07-04-2000
03:00 AM

07-04-2000
03:00 AM

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

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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07-04-2000
03:00 AM

07-04-2000
03:00 AM

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

But adding lots of

Bonnie

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06-01-2003
03:00 AM

06-01-2003
03:00 AM

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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06-01-2003
03:00 AM

06-01-2003
03:00 AM

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

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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06-29-2003
03:00 AM

06-29-2003
03:00 AM

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

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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06-29-2003
03:00 AM

06-29-2003
03:00 AM

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

>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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07-17-2005
03:00 AM

07-17-2005
03:00 AM

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

wow thx it helps