Page 66 - Mathematics Class - XI

Viva-Voce

1. What is the sum of the squares of first n natural numbers?

1
Ans. 1 + 2 + 3 + ... + n = n (n + 1)(2n + 1)
2
2
2
2
6
2. Write the sum of 1 + 2 + ... + 5 .
3
3
3
 55 1( +  2  56×  2
)
Ans. Using formula we get, 1 + 2 + ... + 5 =   2  =  2  = (15) = 225
2
3
3
3



3. Find the sum of cubes of first n even natural numbers.
Ans. We have 2 + 4 + 6 + ... + (2n) 3
3
3
3
= 2 [1 + 2 + 3 + ... + n ]
3
3
3
3
3
 nn( +  2   ( nn + 1  ) 2 
) 1
= 2 ×  2     1 + 2 + + n 3 =  2    
3
3
3
...





= 2[n(n + 1)] 2
4. What is the sum of first n natural numbers?
nn( +1 )
Ans. 1 + 2 + 3 + ... + n =
2
MCQs
1. Series ∑n = 1 then ∑n will be equal to
3
a) 1 b) 2 c) 0 d) –1
2. Sum of the series whose n term is (7n – 5), is given as
th
2
2
a) 7n − 3n 2 b) 7n − 3n c) 7n + 3n d) None of these
2 2 2
n 12 2 .......... up to k terms
2
n
3. If S k , then S = ?
n
k 1 2
n
a) 2 – n – 1 b) 1− 1 c) n 1 1 d) 2 − 1
n
2 n 2 n
n n
4. If r 55 then r will be equal to what value
3
r 1 r 1
a) 3030 b) 6030 c) 3025 d) None of these
7n − 3n 1
2
Answers: 1. a) 1 2. b) 3. c) n 1 4. c) 3025
2 2 n
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