If n is a positive integer, then n ( n2 - 1 ) ( n2 - 4 ) is divisible by _______.
4 x 5 x 6
5 x 6 x 7
2 x 4 x 6
3 x 4 x 5
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
If Pm stands for mPm' then the value of 1 + P1 + 2P2 + 3P3 + ..... + nPn is ______.
n!
n2
( n + 1 )!
( n - 1 ) !
The solution of the inequality is.
( 2/3, 8 )
( -2, 8/3 )
P (n) = P (n + 1 ) for all natural numbers n, then P (n) is ture ?
For all n
For all n > 1
For all n > m
Nothing can be said
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
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
If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
The remainder, when number 599 is dividend by 13, is ______.
2
8
12
32
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
