In an induction proof of the statement 4+7+10+...+(3n-1)=n(3n+5)/2

the first step is to show that the statement is true for some integers n.
Note:3(1)+1=1[3(1)+5]/2 is true. Select the steps required to complete the proof.

A)Show that the statement is true for any real number k. Show that the statement is true for k+1.

B)Assume that the statement is true for some positive integer k. Show that the statement is true for k+1.

C)Show that the statement is true for some positive integers k. Give a counterexample.

D)Assume thst the statement is true for some positive integers k+1. Show that the staement is true for k.
I don't know

Thank you SO much for helping me. I'm not looking for anyone to give me the answer because Ive done the work and what ever I answered is my BEST answer and I can't afford to get them wrong so thanks for all your help from the bottom of my heart.

When I did this yesterday. I assumed it worked at any positive integer and then showed that it worked for n+1 ( Use n = k and n+1 = k+1 to make it clearer)

thanks i got it

Which of the following is a true statement?

A. |–2| < |1|
B. |1| < |0|
C. |–1| < |–2|
D. |1| > |–2|

D. |1| > |-2|

The correct answer is B) Assume that the statement is true for some positive integer k. Show that the statement is true for k+1.

In an induction proof, the goal is to prove that a statement holds for all positive integers (or a subset of positive integers) by using the principle of mathematical induction. This principle has three steps:

1. Base Case: Show that the statement is true for the first integer(s) in the desired range. In this case, the base case is provided as "3(1) + 1 = 1[3(1) + 5]/2 is true."

2. Inductive Hypothesis: Assume that the statement is true for some arbitrary positive integer k. This is the step where you assume that the statement holds true for an initial value, and this assumption is called the inductive hypothesis.

3. Inductive Step: The inductive step is to prove that if the statement holds true for k, then it also holds for the next integer k+1. This step is also called the inductive step because it builds on the assumption made in the inductive hypothesis.

By completing the inductive step, we prove that the statement holds for all positive integers greater than or equal to the base case. Therefore, option B is the correct choice.