For any natural number n, Prove that
Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM
The proof is obtainted by applying principle of mathematical induction.
Let the given statement be
For n = 1, we have
Thus P(1) is true.
Suppose P(k) is true for some positive integer k, i.e.
We shall prove that P(k+1) is also true, i.e.
(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 | 4th Jun, 2014, 03:23: PM
- 17th sum
- What is the use of Binomial Theorem?
- Write the statement of Binomial Theorem for positive integral indices.
- Expandby using binomial expansion.
- Using binomial theorem, evaluate .
- Find the general term in the expansion of :
- Find the middle term in the expansion of :
- Find the middle term in the expansion of .
- Find the term independent of x in the expansion of :
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