Need help writing this as a sum

[toasted]

Homework Statement

Write as a series to represent the infinite sum and write the sum as a rational number.

0.71 + 0.7171 + 0.717171 + 0.71717171...

Please help with this problem. I have been working on it for almost an hour.

 

[jgens]

Are you sure that you've written the problem and/or sum correctly because the particular sum in question (0.71 + 0.7171 + 0.717171 + ...) diverges and consequently is not equal to any real number. Do you perhaps mean write the decimal 0.7171... as an infinite sum and then write this sum as a rational number?

 

[danielatha4]

$$\sum$$ A_k-1+.71*10^-k-(k-1)

Starting on k=2, going to n, and assuming A_k=.71 when k=1

I'm pretty sure about this...

 

[kashiark]

$$\infty$$ i
$$\Sigma$$ $$\Sigma$$ 71*10^(-2a)
i = 1 a = 1

Of this, I am certain. a=1 should be under the second summation.

 

[Mark44]

Homework Statement

Write as a series to represent the infinite sum and write the sum as a rational number.

0.71 + 0.7171 + 0.717171 + 0.71717171...

Please help with this problem. I have been working on it for almost an hour.

I'm with jgens on this. As you have written it, this is a divergent series, so doesn't represent any real number.

Please give us the problem in its exact wording.

 

[HallsofIvy]

$$\infty$$ i
$$\Sigma$$ $$\Sigma$$ 71*10^(-2a)
i = 1 a = 1

Of this, I am certain. a=1 should be under the second summation.

Okay, if you are certain that is the problem, then I am certain if does NOT converge.