Q. 605.0( 1 Vote )

# If then use the principle of mathematical induction to show that for every positive integer n.

Given .

We need to prove that using the principle of mathematical induction.

Step 1: When n = 1, we have    Hence, the equation is true for n = 1.

Step 2: Let us assume the equation true for some n = k, where k is a positive integer. To prove the given equation using mathematical induction, we have to show that .

We know Ak+1 = Ak × A.      Hence, the equation is true for n = k + 1 under the assumption that it is true for n = k.

Therefore, by the principle of mathematical induction, the equation is true for all positive integer values of n.

Thus, for every positive integer n.

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