Principle of Mathematical Induction questions
14 published questions with worked solutions.
- 10^n + 3(4^ n+2 ) + 5 is divisible by (n N)Not in JEE syllabus
- Statement 1: For every natural number n 2, 1 1 + 1 2 + + 1 n > n Statement 2: For every natural number n 2, n(n+1) < n+1Not in JEE syllabus
- If P(n): 2 + 4 + 6 + (2n), n N, then P(k) = k(k+1) + 2 implies P(k+1) = (k+1)(k+2) + 2 is true for all k N. So, statement P(n) =...Not in JEE syllabus
- If A = bmatrix 1 & 0 1 & 1 bmatrix and I = bmatrix 1 & 0 0 & 1 bmatrix , then which one of the following holds for all n 1, by...Not in JEE syllabus
- Using mathematical induction, the numbers a_n's are defined by a_0 = 1, a_ n+1 = 3n^2 + n + a_n, (n 0). Then a_n is equal toNot in JEE syllabus
- Let P(n): n^2 + n + 1 is an even integer. If P(k) is assumed true P(k+1) is true. Therefore, P(n) is trueNot in JEE syllabus
- If P(n) is a statement such that P(3) is true. Assuming P(k) is true P(k+1) is true for all k 3, then P(n) is trueNot in JEE syllabus
- Let P(n) denotes the statement that n^2 + n is odd. It is seen that P(n) P(n+1), P(n) is true for allNot in JEE syllabus
- Statement 1: If P(n) is defined as 2^n < n!, then P(n) is true for all n > 3 Statement 2: In P(n), n may be negativeNot in JEE syllabus
- If P(n) is a statement (n N) such that, if P(k) is true, P(k+1) is true for k N, then p(n) is trueNot in JEE syllabus
- If P(n): 3^n < n!, n N, then P(n) is trueNot in JEE syllabus
- For all n N, 3n^5 + 5n^3 + 7n is divisible byNot in JEE syllabus
- Statement 1: For each natural number n, (n+1)^7-n^7-1 is divisible by 7. Statement 2: For each natural number n, n^7-n is...Not in JEE syllabus
- Let f(n)=10^ n +3 4^ n+2 +5, n N. The greatest value of the integer which divides f(n) for all n isNot in JEE syllabus
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