<h2>
Answer with explanation:</h2>
We are asked to prove by the method of mathematical induction that:

where n is a positive integer.
then we have:

Hence, the result is true for n=1.
- Let us assume that the result is true for n=k
i.e.

- Now, we have to prove the result for n=k+1
i.e.
<u>To prove:</u> 
Let us take n=k+1
Hence, we have:

( Since, the result was true for n=k )
Hence, we have:

Also, we know that:

(
Since, for n=k+1 being a positive integer we have:
)
Hence, we have finally,

Hence, the result holds true for n=k+1
Hence, we may infer that the result is true for all n belonging to positive integer.
i.e.
where n is a positive integer.
Answer: 2/5
Step-by-step explanation: Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction
Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes
The, multiply the numerators and denominators and get 12/30, then simply by 6 and get 2/5
Let
x = first consecutive odd
x + 2 = second consecutive odd
Based on the problem, we equate
x + (x + 2) = 32
Solving for x,
2x + 2 = 32
2x = 32 - 2
2x = 30
x = 30/2
x = 15
and x + 2 = 15 + 2 = 17
Therefore, the integers are 15 and 17.
<span>122.40 is the answer. I hope this helps :) Please give me a rate and Thanks :)</span>