Three way tug of war vectors

If the ring is not moving, vectors a+b+c=0


    Three way tug of war vectors:

Geometric series convergence and divergence examples

Convergence occurs when 0< |r| <1
Geometric series convergence and divergence examples:

One-sided limits from graphs

When approaching from the -ve side, there is a negative superscript for the limit number


    One-sided limits from graphs:

Function as geometric series

Find the common ratio r.

convergence occurs if  -1 < r < 1

For such an interval of convergence, S=a/(1-r)

  Function as geometric series:

Tangent slope as limiting value of secant slope example 1

Draw out the graph to see what is needed.
It may be possible to substitute algebraically to get the solution.


    Tangent slope as limiting value of secant slope example 1:

Relatively prime numbers

In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also spelled co-prime)^[1] if the only positive integer that evenly divides both of them is 1. That is, the only common positive factor of the two numbers is 1. 

For example, 14 and 15 are coprime, being commonly divisible by only 1, but 14 and 21 are not, because they are both divisible by 7.