How many 4 digit numbers can be created from the digits 7.3.1,8,3 and 4
1 answer:
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Answer:
option 1 both statements are true
Step-by-step explanation:
Prove by PMI -- Principle of Mathematical Induction
1) n³ + 2n
n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1 ---->divisible by 3
n = 2 ; 2³ + 2*2 = 8+4 = 12 = 3*4 ----> is divisible by 3
Assume that It is valid for n = k ;
= 3*m -----(I) , for all m ∈ N
We have to prove for n =k +1 , the statement is true.
n = k+1,
= k³ + 3k² + 3k + 3 + 2k
= k³ + 2k + 3k² + 3k + 3
= 3m + 3 (k² + k + 1)
= 3(3 + [k² + k + 1] ) is divisible by 3
Therefore, this statement is true
2)
This statement is also true