Prove that the product of two consecutive natural numbers is an even umber using the principal of mathematical induction
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Answered by
1
see 9+9= 18
4+4= 8
6+6=12
8+8=16
and so on and so forth ever consecutive number is an even number
4+4= 8
6+6=12
8+8=16
and so on and so forth ever consecutive number is an even number
Answered by
8
Let P(n): n(n+1) is even
Now
P(1): 1.2=2 is even is true
P(n+1): (n+1)(n+2) is even
(n+1)(n+2)= n(n+1)+2((n+!) which is sum of two even numbers since n(n+1) is even by P(n) conjecture and 2(n+1) is also even being multiple of 2
Thus P(n)⇒P(n+1)
which proves the proposition
Now
P(1): 1.2=2 is even is true
P(n+1): (n+1)(n+2) is even
(n+1)(n+2)= n(n+1)+2((n+!) which is sum of two even numbers since n(n+1) is even by P(n) conjecture and 2(n+1) is also even being multiple of 2
Thus P(n)⇒P(n+1)
which proves the proposition
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