Which of the following best describes the term induction?
o
a. writing down the steps to solve a complicated math problem
b. forming rules based upon observations and experiences
c. starting with a given set of rules and figuring out what must be
true
o
d. reducing the solution to a problem in lowest terms

C. Starting with a given set of rules and figuring out what must be  true . TRUE

Step by step explanation:

Mathematical Induction

Mathematical Induction is a mathematical technique which we can use to prove any given mathematical statement, result, theorem or corollary with help of induction.

Here, we assume the statement to be true for a smaller natural number            (Usually 1) and then prove the statement to be true for ANY ARBITRARY NUMBER say k.

Now, from the given options:

A. Writing down the steps to solve a complicated math problem .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.

B. Forming rules based upon observations and experiences .

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  We need to induce the needed  statement or Result.

C. Starting with a given set of rules and figuring out what must be  true .

TRUE as the induction method is based on ASSUMPTION and INDUCTION.

We try and find out  the result with the given existing data.

D. Reducing the solution to a problem in lowest terms.

FALSE as the induction method is based on ASSUMPTION and INDUCTION.  

Step-by-step explanation:

Since we're finding the product, we have to multiply:

×

You can simplify in this stage by using the "butterfly method", and dividing by , and by , you'd then have:

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Multiply the numerators and the denominators to get:

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If you prefer the longer way, again, multiply:

×

Multiply the numerators and the denominators:

Simplify the fraction by dividing both the numerator and denominator by :