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Grade: 11
        
using principle of mathematical induction prove that n^3-7n+3 is divisible by 3
one year ago

Answers : (1)

Vishal Khule
15 Points
							
Let p(n):n^3-7n+3 is divisible by all natural number n
Now, P(1)=(1)^3-7(1)+(3)=-3 is divisible by 3
Hence, P(1) is true. 
Now assume that P(n) is true for some natural
number n=k
Then P(n)=n³-7n+3 is divisible by 3.
Or n³-7n+3=3m,for m Is in N
Now consider, 
P(k+1)=(k+1)^3-7(k+1)+3
            =K³+1+3k²+3k-7k-7+3
           =k³-7k+3+3k(k+1)-6
            =3m+3k(k+1)-6
            =3(m+k(k+1)-2)
            =3M ,where, M=m+k(k+1)-2
Therefore, P(k+1) is divisible by 3
Hence, By principal of mathematical induction P(n) is true for all natural number n  
            
 
one year ago
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