-1
votes
3answers
152 views

What's wrong with using algebra on infinite series?

I've recently found an article (referred somewhere on this site) criticizing the use of common rules of algebra on infinite series. To be honest, the video referred is one of the videos of Numberphile ...
6
votes
2answers
86 views

Is $\frac{0}{0}$ different from $\frac{1}{0}$?

In my mind, zero divided by zero answers the question of what $a$, when multiplied with zero, equals zero: $a * 0 = 0$ Obviously, any real number will satisfy this equation. However, one divided by ...
0
votes
3answers
153 views

Why does $0,\bar{9}$ equal $1$? [duplicate]

I am finding hard to understand why $0,99999..... = 1$ I have the following proof: Let $x$ be $0,9999...$ then $10x = 9,999...$ So $10x - x = 9,999 - 0,9999$ $9x = 9 \rightarrow x = 1$ From a ...
1
vote
0answers
70 views

Simplifying this infinite series [duplicate]

Possible Duplicate: How can I evaluate $\sum_{n=1}^\infty \frac{2n}{3^{n+1}}$ I have an infinite series like so: $$\sum_{i=0}^\infty (i+1)x^i$$ or basically $$ 1 + 2x + 3x^2 + 4x^3 +... ...
3
votes
2answers
332 views

How many times more than $0$?

If I have $10$ apples, but you have $5$ apples, then I have $2$ times more apples than you. But what if I have $10$ apples, but you don't have any apples? If you look at the graph ...
44
votes
7answers
11k views

Infinity = -1 paradox

I puzzled two high school Pre-calc math teachers today with a little proof (maybe not) I found a couple years ago that infinity is equal to -1: Let x equal the geometric series: $1 + 2 + 4 + 8 + 16 ...