Let P(n) be a statement and let P(n)⇒P(n+1) for all natural numbers n, then P(n) is true for
Let P(n) be a statement 2^{n}<n!, where n is a natural number, then P(n) is true for
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If x > 1, then the statement (1+x)^{n}>1+nx is true for
The smallest +ve integer n , for whichn!
If P (n) = 2+4+6+………………..+2n , n ∈ N , then P (k) = k (k + 1) + 2 ⇒ P (k + 1) = (k + 1) (k +2) + 2 for all k ∈ N. So we can conclude that P (n) = n (n + 1) +2 for
x(x^{n1}  na^{n1})+ a^{n} (n1) is divisible by (xa)^{2} for
The greatest positive integer, which divides n (n + 1) (n + 2) (n + 3) for all n ∈ N, is
Let P (n) denote the statement n^{2}+n is odd, It is seen that P(n) ⇒ P(n+1), therefore P (n) is true for all
The greatest positive integer, which divides (n+1)(n+2)(n+3)..................(n+r) ∀n∈W, is
The statement P (n) : “1 X 1! + 2 X 2! + 3 X 3! + …..+ n X n! = (n + 1) !..... 1 “ is
A student was asked to prove a statement P (n) by method of induction. He proved that P (3) is true and that P(n) ⇒ P(n+1) for all natural numbers n. On the basis of this he could conclude that P (n) is true
3^{2n+2}−8n−9is divisible by 64 for all
The statement 3^{n}>4n is true for all
The statement 2^{n}>3n is true for all
The statement 2^{n+2}<3^{n} is true for all
The smallest positive integer for which The statement 3^{n+1}<4^{n} is true for
For all n ∈ N , 49^{n}+16n−1 is divisible by
The digit in the unit’s place of the number 183! + 3^{183} is
7^{2n}+3^{n−1}.2^{3n−3} is divisible by
If n ∈ N then n^{3}+2n is divisible by
If n is a positive integer , then 2.7^{n}+3.5^{n}−5 is divisible by
If n is a +ve integer, then 4^{n}−3n−5 is divisible by
If n is a +ve integer, then 2.4^{2n+1}+3^{3n+1} is divisible by
If n is a +ve integer, then 10^{n} +3.4^{n+2} + 5 is divisible by
447 docs930 tests

Test: Applications Of Mathematical Induction Test  15 ques 
Test: Introduction To Mathematical Induction Test  10 ques 
Test: Principle Of Mathematical Induction 2 Test  25 ques 
JEE Advanced (Single Correct Type): Mathematical induction & Binomial Theorem Doc  8 pages 
JEE Advanced (One or More Correct Option): Mathematical induction & Binomial Theorem Doc  3 pages 
447 docs930 tests

Test: Applications Of Mathematical Induction Test  15 ques 
Test: Introduction To Mathematical Induction Test  10 ques 
Test: Principle Of Mathematical Induction 2 Test  25 ques 
JEE Advanced (Single Correct Type): Mathematical induction & Binomial Theorem Doc  8 pages 
JEE Advanced (One or More Correct Option): Mathematical induction & Binomial Theorem Doc  3 pages 