10 2 n − 1 + 1 for all n ∈ N is divisible by
The product of three consecutive natural numbers is divisible by
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 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
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?
Let x > − 1 , then statement P ( n ) : ( 1 + x ) n > 1 + n x is true for
