Please solve the following
Asked by manasd | 17th Sep, 2015, 10:34: PM
Answered by satyajit samal | 18th Sep, 2015, 02:50: PM
- Q-6 in the image
- Prove 10th by mathatical induction
- Prove by using the principle of mathematical induction 32n – 1 is divisible by 8 for n N.
- Prove by using the principle of mathematical induction n(n + 1)(n + 2) is divisible by 6 for all n N.
- If P(n) is the statement ‘22n – 1 is multiple of 3’ then show that P(5) is true.
- Let P(n) be the statement," n3 + n is divisible by 3". Check whether P(3) and P(4) is true.
- Prove by using the principle of mathematical induction 3n < 4n for all n N.
- If P(n) is the statement 72n + 23n - 3.3n - 1 is divisible by 25 for all n N, then what is P(k + 1)?
- Show that if statement P(n): 2 + 4 + 6 + --- + 2n = n( n + 1) + 2 is true for n = k, then it is also true for n = k + 1. Can we apply the principle of mathematical induction?
- Prove that 102n – 1 + 1 is divisible by 11 for all n N.
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