There is nothing wrong with the proof, it is in fact true that .
Note: If this thread starts getting "philosophical" , just be warned, you know I hate that stuff and I will close it.
Let me teach you some of the basics of a geometric series...
The difference between a sequence and a series is:
Series:
Sequence:
A geometric series is formed by multiplying each term by a constant.
For example:
Could also be written as:
The n-th term is equal to:
is the starting term, the first term (a = 1 in the example).
is the common ratio (r = 2 in the example).
You can determine with the following formula:
In series and sequences, the Sigma-sign is very important.
Now i do hope that's all...
Hello, jtl!
There's nothing wrong with that proof.
Let
This is a geometric series with first term and common ratio
. . Its sum is: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Another proof
We have: .
Multiply by 10: .
. . Subtract : . .
And we have: .