- #1

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## Main Question or Discussion Point

we have to prove that

10+100+1000+10000+100000+.........=-(1/9)

any ideas?

10+100+1000+10000+100000+.........=-(1/9)

any ideas?

- Thread starter sutupidmath
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- #1

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we have to prove that

10+100+1000+10000+100000+.........=-(1/9)

any ideas?

10+100+1000+10000+100000+.........=-(1/9)

any ideas?

- #2

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10+100+1000+10000+100000+.........=-(10/9)

here is a "proof" :)

let

S = 10 + 100 + 1000 + 10000 + ...

then

10S = 100 + 1000 + 10000 + ...

now,

S - 10S = 10

=> -9S = 10

=> S = -(10/9)

=> 10 + 100 + 1000 + 10000 + ... = -(10/9)

- #3

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i dunno maybe this is what i actually was looking for.

- #4

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- #5

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so Murshid_islam what is the deal here? I can see that the series does not converge, however where is the problem on your proof? Is there a mathematical error, cause i could not see it, or what can we say about this?

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- #7

arildno

Science Advisor

Homework Helper

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Because, in his expression for 10S, he ignored the largest term present there.

- #8

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as long as we are talking for infinit large numbers i cannot grasp how could there be a larger number on 10S than on S.I think it is absurd to talk about a "largest"term here, as long as we deal with infinit large terms! however i do understand the error now. SO defenitely we can say that

10+100+1000+10000+100000+.........=-(10/9)

is not mathematically true, and i cannot count on it, right?

10+100+1000+10000+100000+.........=-(10/9)

is not mathematically true, and i cannot count on it, right?

Last edited:

- #9

HallsofIvy

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Homework Helper

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Yes, I recommend that you not count on it!

- #10

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why don't you use sum of infinite G.P?

- #11

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can you tell me?

- #12

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Yeah, i also thought it could not be negative. However i saw this on a tv scientific show, and a proffesor demonstrated this, so i just wondered how that would be possible. That proffesor, whose name i cannot remember, said that he had turned this for a mathematical test to prove that this is right. If ,at first place, this is exactly what i saw, couse i am not 100% posotive.I would have thought it obvious from the start that a sum of positive numbers cannot be negative!

!

- #13

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G.P - Geometric Progression

can you tell me?

It is a series in which each term, apart from the first, is a fixed multiple of the previous term.

a + ar + ar^2 + ar^3 + ...+ar^n+...

The sum of the first n terms of such a series is a(1-r

- #14

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thnx indeed.

- #15

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- #16

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Yes, it diverges.

But, as mentioned earlier, the thing that should first convince you that the statement is not true is that the a sum of positive numbers cannot give you a negative number.

- #17

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yeah, thank you guys for your help.

- #18

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the error was when i let S = 10 + 100 + 1000 + .....so Murshid_islam what is the deal here? I can see that the series does not converge, however where is the problem on your proof? Is there a mathematical error, cause i could not see it, or what can we say about this?

As the series doesn't converge i cannot let it equal to a number S.

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