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 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
The value of ( 1 x 2 x 3 ) + ( 2 x 3 x 4 ) + ( 3 x 4 x 5 ) + ..... + n terms is ______.
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
If x > y > 0 where a > 1, then ?
log ax > logay
logax < logay
logax ≥ logay
log ax = log ay
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 number 101 x 102 x 103 x 104 x ..... x 107 is divisible by ______.
4000
4050
5040
5050
The remainder, when number 599 is dividend by 13, is ______.
2
8
12
32
If equation (5 + 2 √6)n = i + f, Where i ∈ N, 0 < f < 1, then value of ( i + f ) ( 1 - f) is ______.
0
1
72n
22n
If log2 7 = x, then x is ________.
An irrational number
A rational number such that 0 < x < 2
A prime number of the form 7n + 2
A rational number such that 2 < x < 3
