1+11+111+1111+11111....
the geometric series can be summed to infinity. Find this sum

Question

1+11+111+1111+11111....
the geometric series can be summed to infinity. Find this sum

anonymous · Answer

this will be diverge but only thing we can do is to find sum of  $n$ term

terenzreignz · Answer

But this isn't a geometric series to start with, is it?

dls · Answer

Hint:Multiply divide by 9

anonymous · Answer

and also this not a GP

anonymous · Answer

how do you find the sum of the n term

dls · Answer

Guys this isn't GP! We have to convert it into GP!
For this:
Multiply Divide by 9:
9+99+999+9999+99999..../9
Now we can write 9 as 10-1 and 99 as 100-1 ...and so on..So now this is GP .
Now use the infinite sum formula:
S=a(r^n-1)/r-1
You have the answer :)

anonymous · Answer

thanks!

terenzreignz · Answer

I think the sum of the first n terms is

$$\sum_{k=0}^{n}(n-k)10^{k}$$

terenzreignz · Answer

I don't think what @DLS did actually made it into a Geometric Series...
Unless I'm missing something
If I am, please enlighten me :(

anonymous · Answer

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