CBSE Class 11-science Maths Introduction to Mathematical Induction

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• By using principle of mathematical induction, prove that: 1 + 4 + 7 + --- + (3n - 2) =n(3n-1)
• Let P(n) be the statement `n(n + 1) is an even number’ then find P(6).
• If P(n) be the statement `12n + 3’ is a multiple of 5, then show that P(3) is false, whereas P(6) is true.
• Let P(n) be the statement `n² + n is even’. If P(k) is true , then show that P(k + 1) is true.
• Let P(n) be the statement . If P(k)    is true,then show that P(k+1) is true.
• Explain the principle of mathematical induction:
• If  P(n) be the statement ‘n² – n + 41 is a prime number’, then show that P(1), P(2) are true but P(41) is not true.
• Show by using principle of mathematical induction, prove that: 1 + 2 + 3 + -----+ n =
• Let P(n) be the statement , If P (k) is true , then show that P(k + 1) is true.

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