Permutation and Combination – Class XI – Exercise 7.1 — Breath Math

1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) Repetition of the digits is allowed? (ii) Repetition of the digits is not allowed? Solution: (i) There will be number of ways of filling 3 vacant places in succession by the given five digits. Here, […]

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Principle of Mathematical Induction – Class XI – Exercise 4.1[Part 2] — Breath Math

11: Prove the following by using the principle of mathematical induction for all n€ N: 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + … +1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2) Solution: Let the given statement be P(n), i.e., P(n): 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + … +1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2) For n = 1, we have P(1): 1/1.2.3 = 1.(1+3)/4(1+1)(1+2) = […]

via Principle of Mathematical Induction – Class XI – Exercise 4.1[Part 2] — Breath Math