Using mathematical induction prove whether or not the following statement is true for all positive integers n, or show why it is false.

2+6+10+ +4n-2=2n^2

Base case: For , the left side is 2 and the right is , so the base case holds.

Induction hypothesis: Assume the statement is true for , that is

We want to show that this implies truth for , that

The first terms on the left reduce according to the assumption above, and we can simplify the -th term a bit:

so the statement is true for all .

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

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step-by-step explanation: