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What is the second step to prove that Sn=>2+2^2+2^3+...+2^n=2(2^n-1)?

Show that is valid for n = k + 2.
Assume that is valid for n = k and prove that is valid for n = k + 1.
Show that is valid for n = k.
Verify that is valid for n = 1.

Respuesta :

Answer:

Assume that Sn is valid for n = k and prove that Sn is valid for n = k + 1.

Step-by-step explanation:

This is the second step in the principal of mathematical induction. The three steps in the principals of mathematical induction are:

1. show that something works for the first case (base or anchor step)

2. assume that it works for any particular step (inductive hypothesis), and then

3. show that it works for the next case (inductive step)

p. 621 in textbook

It's weird that they put steps 2 & 3 together, but it was correct on the test so ¯\_(ツ)_/¯

The second step to prove principle of mathematical induction is "Assume that is valid for n = k and prove that is valid for n = k + 1".

What is principle of mathematical induction?

Principle of mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n.

Step 1:  Check whether the given statement is true for n = 1.

Step 2: Assume that given statement P(n) is also true for n = k, where k is any positive integer. Prove that the result is true for P(k+1) for any positive integer k.

Learn more about principle of mathematical induction here

https://brainly.com/question/24393371

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