Prove that if a|b and b|c, then a|c.

Interpreting z-scores: Complete the following statements using your knowledge about z-scores.
a. If the data is weight, the z-score for someone who is overweight would be
-positive
-negative
-zero
b. If the data is IQ test scores, an individual with a negative z-score would have a
-high IQ
-low IQ
-average IQ
c. If the data is time spent watching TV, an individual with a z-score of zero would
-watch very little TV
-watch a lot of TV
-watch the average amount of TV
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be
-positive
-negative
-zero

Evaluate fraction of sum
So i have to evaluate this sum:
${\displaystyle \frac{1-2^{-2}+4^{-2}-5^{-2}+7^{-2}-8^{-2}+{10}^{-2}-{11}^{-2}+\cdots }{1+2^{-2}-4^{-2}-5^{-2}+7^{-2}+8^{-2}-{10}^{-2}-{11}^{-2}+\cdots }}$
it has the form : ${\displaystyle \frac{\sum _0^{\mathrm{\infty }}[{(3n+1)}^{-2}-{(3n+2)}^{-2}]}{\sum _0^{\mathrm{\infty }}{(-1)}^n[{(3n+1)}^{-2}+{(3n+2)}^{-2}]}}$
My current attempt : Trying to convert this into power series
${\displaystyle a\left(n\right)={(3n+1)}^{-2}-{(3n+2)}^{-2}b\left(n\right)={(3n+1)}^{-2}+{(3n+2)}^{-2}}$
Can a(n) and b(n) be the definite integral of certain polynomial function f(x) ?
Maybe there is a better direction. Can someone give me a hint ?

To find:
The ratio of the width to the perimeter of the swimming pool.
The length and width of swimming pool is given as 45 feet and 30 feet respectively.

1. Why are units so important in measurement? Giving examples of measurements with no units should help.
2. What does it mean to say that 2 expressions are equivalent?

Intuitively, why does ${\displaystyle \frac{a}{c}}={\displaystyle \frac{1}{\frac{c}{a}}}$?
For intuition, I reference objects. Imagine making a dessert with: $a$ as apples and $c$ as chestnuts.
Question. How and why is
${\displaystyle \frac{a}{c}}(3)={\displaystyle \frac{1}{{\displaystyle \frac{c}{a}}}}(4)?$
I ask only about intuition; please omit formal arguments and proofs (eg: Intuition is not generated by the explanation that rationalising (4)'s denominator produces (3)).

How do you combine like terms in ${\displaystyle 7x^2-7x+5+4x^2+9x-6}$?

$3x-3=10$. Find x.