Class : 11 (Mathematics)

Topics - Mathematical InductionAllotted Time: 45 min Max. Marks: 30

General Instructions:

1. All Questions are compulsory. Marks are indicated against each question.

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Q1. Prove that 3

2 2 21 2 ... , N3nn n (4)

Q2. Prove that 1 1nx nx , for all natural number n, where x > – 1 (4)

Q3.

1 1 1 21 ...1 2 1 2 3 1 2 3 ... 1

nn n

(4)

Q4. 1

2 3 2 1 3 31.3 2.3 3.3 ... .3

4

nn n

n

(4)

Or

2 2 11.2 2.2 3.2 ... .2 1 2 2n nn n

Q5. 2

2

2 13 5 71 1 1 ... 1 11 4 9

nn

n

(4)

Q6. 1 5n n n is a multiple of 3. (4)

Q7. Prove that 2.7 3.5 5n n is divisible by 24, for all Nn (6)