Question

$- 4n( - 2n - 3) - 2n(1 + 2)$
​

Answer 1

Answer:

The first item, (2n+1)+(2n+3)+(2n+5)+⋯+(4n−1)

=(1+3+5+⋯+(4n−1))−(1+3+5+⋯+(2n−1))

comes because you are just adding and subtracting the same set of terms on the RHS.

Your base case for the induction has just one term on the left side, which I would write 2∗1+1=3∗12 For the induction, assume (2n+1)+(2n+3)+(2n+5)+⋯+(4n−1)=3n2 then extend it to n+1: (2n+1)+(2n+3)+(2n+5)+⋯+(4n−1)+(4n+1)+(4n+3)−(2n+1)

=3n2+4n+1+4n+3−(2n+1)=3n2+6n+1=3(n+1)2

Answer 2

Step-by-step explanation:

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