The statement P (n ): ( 1 x 1! ) + (2 x 2! ) + (3 x 3! ) + .... + ( n x n !) = ( n + 1 )! - 1' is _____.
True for all values of n > 1
Not true for any value of n
True for all values of n ∈ N
None of these
A student was asked to prove a statement P (n) by method of induction. He proved that P (3 ) is true such that
P (n) = P (n + 1 ) for all ______.
n ∈ N
n ≥ 3
n ∈ I
n < 3
The unit digit in the number 7126 is ______.
1
3
9
5
If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
The total number of proper divisors of 38808 is _______.
80
70
60
50
If equation (5 + 2 √6)n = i + f, Where i ∈ N, 0 < f < 1, then value of ( i + f ) ( 1 - f) is ______.
0
72n
22n
The expression 3 2n + 2 - 8n - 9 is divisible by 64 for all ______.
n ∈ N, n < 2
n ∈ N n ≥ 2
n ∈ N, n > 2
By the method of mathematic induction, the inequality 2n + 7 ≤ ( n + 3 ) 2 is true ?
For all n ∈ N
For all n < 1
Only when n is odd
Only when n is even
By the mathematical induction, the expression 11n+2 + 122n + 1 is divisible by _______.
133
124
114
113
All possible two - factor products are from the digits 1,2,3,4, ...., 200. The number of factors out of the total obtained, which are multiples of 5, is _______.
8040
7180
6150
4040
