Q. 235.0( 1 Vote )

# Using the princip

To Prove:

Let us prove this question by principle of mathematical induction (PMI) for all natural numbers

Let P(n):

For n = 1 P(n) is true since , which is true

Assume P(k) is true for some positive integer k , ie,

= …(1)

We will now prove that P(k + 1) is true whenever P( k ) is true

Consider ,

[ Using 1 ]

[Multiplying and dividing by 2 on RHS ]

Now ,

Therefore, P (k + 1) is true whenever P(k) is true

By the principle of mathematical induction, P(n) is true for all natural numbers, ie, N.

Hence proved.

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