Principle Of Mathematical Induction Questions for CBSE Class 11th

# Principle Of Mathematical Induction Questions for CBSE Class 11th

10 2 n − 1 + 1 for all n ∈ N is divisible by

The product of three consecutive natural numbers is divisible by

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For all odd positive integer n , the number n n 2 − 1 is divisible by

For all n ∈ N , 2 ⋅ 4 2 n + 1 + 3 3 n + 1 is divisible by

If 49 n + 16 n + λ is divisible by 64 for all n ∈ N , then the least negative integral value of λ , is

If A = 1 1 1 1 1 1 1 1 1 then A n for every positive integer n is

If 7 103 is divided by 25, then the remainder is

For all n ∈ N , 1 × 1 ! + 2 × 2 ! + 3 × 3 ! + … + n × n ! is equal to

For all n ∈ N , 3 3 n − 26 n − 1 is divisible by

The identity 1 3 + 2 3 + 3 3 + … + n 3 is equal to

2 3 n − 7 n − 1 s divisible by

The sum of series 1+2+3+………n is less than

If u n + 1 = 3 u n − 2 u n − 1 and u 0 = 2 , u 1 = 3 then u n s equal to

For n ∈ N , 1 5 n 5 + 1 3 n 3 + 7 15 n is

For all n ∈ N , n ( n + 1 ) ( n + 5 ) is a multiple of

The value of 1 + 3 1 1 + 5 4 1 + 7 9 ⋯ 1 + 2 n + 1 n 2 is

The sum of series 1 ⋅ 3 + 2 ⋅ 3 2 + 3 ⋅ 3 3 + … + n ⋅ 3 n is

lf P(n) is a statement such that P(3) is true. Assuming P(k) is true ⇒ P ( k + 1 ) is true for all k ≥ 3 then P(n) is true

Let P ( n ) : n 2 + n + 1 is an even integer. If p(k) is assumed true ⇒ P ( k + 1 ) is true. Therefore, P(n) is TRUE

By mathematical induction 1 1 ⋅ 2 ⋅ 3 + 1 2 ⋅ 3 ⋅ 4 + … + 1 n ( n + 1 ) ( n + 2 )

By principle of mathematical induction cos ⁡ θcos ⁡ 2 θcos ⁡ 4 θ … cos ⁡ 2 n − 1 θ , ∀ n ∈ N =

The smallest positive integer n for which n ! < n + 1 2 n holds , is

Let S ( K ) : 1 + 3 + 5 + … + ( 2 K − 1 ) = 3 + k 2 Then which of the following is true?

If a , b , c , ∈ N , a n + b n is divisible by c when n is odd but not when n is even, then value of c is

If a n = 7 + 7 + 7 + ⋯ having n radical signs then by methods of mathematical induction which of the following is true

Let x > − 1 , then statement P ( n ) : ( 1 + x ) n > 1 + n x is true for

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