- #1

Purpleshinyrock

- 27

- 6

- TL;DR Summary
- sequences,

Hello, I am currently self studying sequence and series and I got to a topic called arithmetic-geometric sequence, and after the theory It gives this exercise:

1) Find the sum:

S=1+11+111+1111+...+111...111, if the last (number) is a digit of n.

I was given a tip That says that

1 = (10 - 1)/9

11 = (100 - 1)/9 = (102 -1)/9

111 = (1000 - 1)/9 = (103 -1)/9

...

1111...111 = (100..000 - 1)/9 = (10n -1)/9

But I don't get how They got to this law of formation, did they apply a formula, what did they do?

Could You please help me?

Your time is appreciated.

Thank You.

1) Find the sum:

S=1+11+111+1111+...+111...111, if the last (number) is a digit of n.

I was given a tip That says that

1 = (10 - 1)/9

11 = (100 - 1)/9 = (102 -1)/9

111 = (1000 - 1)/9 = (103 -1)/9

...

1111...111 = (100..000 - 1)/9 = (10n -1)/9

But I don't get how They got to this law of formation, did they apply a formula, what did they do?

Could You please help me?

Your time is appreciated.

Thank You.