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For any natural number n, Prove that .
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
The proof is obtainted by applying principle of mathematical induction.
Let the given statement be
P(n):
For n = 1, we have
P(1) :
Thus P(1) is true.
Suppose P(k) is true for some positive integer k, i.e.
(1)
We shall prove that P(k+1) is also true, i.e.
Now,
= (a+b)

[From (1)]
(By actual multiplication)
[grouping like terms]

Thus, it has been proved that P(k +1) is true whenever P(k) is true.
By principle of mathematical induction, P(n) is true for every positive integer n.
Answered by | 04 Jun, 2014, 03:23: PM

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