# Thread: Converging of Digits proof

1. ## Converging of Digits proof

Let (d sub k) from k=1 to inf be a sequence of digits. Then

Summation from j=1 to inf { (d sub j) * (10^-j) } converges.

Any idea on how to complete this proof? Any help is appreciated!

2. Originally Posted by jstarks44444
Let (d sub k) from k=1 to inf be a sequence of digits.

So $\{d_k\}_{k=1}^\infty\,,\,\,d_k=0,1,2,...,9\,\,\for all k$

Then

Summation from j=1 to inf { (d sub j) * (10^-j) } converges.

Then $\displaystyle{\sum\limits^\infty_{k=1}\frac{d_k}{1 0^k}}$ converges

Any idea on how to complete this proof? Any help is appreciated!

The series is an infinite positive one, so why don't you try to bound it up from above...say, by a converging geometric series...?

Tonio