Page 59 - Mathematics Class - XI

Viva-Voce

1. What is the sum of squares of first five natural numbers?
1
Ans. We know that the sum of the squares of n natural numbers = n (n + 1) (2n + 1)
Here, n = 5 6

1
1
= × 5 × (5 + 1) × (2 × 5 + 1) = × 5 × 6 × 11 = 55
6 6
2. What is meant by a sequence?
Ans. By a sequence, we mean arrangement of number in definite order according to some rule.
Also, we define a sequence as a function whose domain is the set of all natural numbers or some subsets
of the type {1, 2, 3, ... n}.

3. What do you understand by finite and infinite sequences?
Ans. A sequence containing a finite number of terms is called a finite sequence.
A sequence is called an infinite if it is not a finite sequence.

4. Write the formula for the series: 2 + 4 + 6 + ... + (2n) .
2
2
2
2
Ans. 2 + 4 + 6 + ... + (2n) = (2 × 1) + (2 × 2) + (2 × 3) + ... + (2 × n) = 2 (1 + 2 + 3 + ... + n )
2
2
2
2
2
2
2
2
2
2
2
2
2
4nn( + 1 2n)( + 1) 2nn( + 1 2n)( + 1) 1
= = [⸪ 1 + 2 + 3 + ... + n = n(n + 1) (2n + 1)]
2
2
2
2
6 3 6
5. What is the sum of the squares of first 20 natural numbers?

Ans. Sum of squares of 1 to 20 natural numbers 1 [ 20 20( 12)( 20 1)] 1 20 21 41 2870
6 6
MCQs
1. If Σn = 1 then Σn will be equal to
2
a) 1 b) 2 c) 3 d) 4
2. The sum of the series up to 1 + 3 +5 + .............. + n terms is equal to
2
2
2

a) n 2 n 1 2 b) n 2 n 1 2 n 1 c) n n 12 n 1 d) nn 1

3 3 6 2
3. The sum of the series 1 + 2 + 3 + 4 + .......... + n is equal to
) 1
a) n b) nn( 2 c) nn( +1 ) d) None of these

2 n 1+ 2 2
4. If the n term of the given series is (n + 3 ) then the sum of that series upto n terms is
n
2
th
3
)(
)(
3
a) nn( 12 n 1 ) 3 n 1 b) nn( 12 n 1 ) 3 n 1 1
6 2 6 2
3
c) nn( 1 ) 3 n 1 d) None of these
2 2
n
3
)(
Answers: 1. a) 1 2. b) 2 n 1 2 n 1 3. c) nn( +1 ) 4. a) nn( 12 n 1 ) 3 n 1
3 2 6 2
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