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

Vishal Khule
15 Points
```							Let p(n):n^3-7n+3 is divisible by all natural number nNow, P(1)=(1)^3-7(1)+(3)=-3 is divisible by 3Hence, P(1) is true. Now assume that P(n) is true for some naturalnumber n=kThen P(n)=n³-7n+3 is divisible by 3.Or n³-7n+3=3m,for m Is in NNow 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)-2Therefore, P(k+1) is divisible by 3Hence, By principal of mathematical induction P(n) is true for all natural number n
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one year ago
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• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions