Home
Class 11
MATHS
Prove the rule of exponents (a b)^n=a^n ...

Prove the rule of exponents `(a b)^n=a^n b^n`by using principle of mathematical induction for every natural number.

Text Solution

Verified by Experts

Let P(n) be the given statement i.e., P(n):`(ab)^n=a^nb^n`
We note that P(n) is true for n=1 since `(ab)^1=a^1b^1`.
Let P(k) be true, i.e., `(ab)^k=a^kb^k`----------(1)
We shall now prove that `P(k+1)` is true whenever `P(k)` is true.
...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT|Exercise EXERCISE 4.1|24 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT|Exercise EXERCISE 7.2|5 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 16.3|21 Videos

Similar Questions

Explore conceptually related problems

Using principle of mathematical induction prove that sqrt(n) =2

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

Prove by using principle of mathematical induction :2^(n)<3^(n),n in N

Using the principle of mathematical induction, prove that n<2^(n) for all n in N

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Prove by the principle of mathematical induction that for all n in N,n^(2)+n is even natural number.

Prove the following by using the principle of mathematical induction. n(n+1)+1 is an odd natural number, n in N .

Prove by the principle of mathematical induction that n<2^(n) for alln in N

Prove the following by using the Principle of mathematical induction AA n in N 3^(n)>2^(n)

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

Home
Profile