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Class 11-commerce NCERT Solutions Maths Chapter 8 - Sequences and Series

Sequences and Series Exercise Ex. 8.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Sequences and Series Exercise Ex. 8.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5



Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16


Solution 17

Solution 18

Solution 19

Solution 20

Solution 21


Solution 22

Solution 23

Solution 24

Solution 25

a, b, c, d are in G.P.

Therefore,

bc = ad      .....(1)

b2 = ac      .....(2)

c2 = bd      .....(3)

It has to be proved that,

(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2

R.H.S.

= (ab + bc + cd)2

= (ab + ad + cd)2  [Using (1)]

= [ab + d (a + c)]2

= a2b2 + 2abd (a + c) + d2(a + c)2

= a2b2 + 2a2bd + 2abcd + d2(a2 + 2ac + c2)

= a2b2 + 2a2c2 + 2b2c2 + d2a2 + 2d2b2 + d2c2  [Using (1) and (2)]

= a2b2 + a2c2 + a2c2 + b2c2 + b2c2 + d2a2 + d2b2 + d2b2 + d2c2

= a2b2 + a2c2 + a2d2 + b2 × b2 + b2c2 + b2d2 + c2b2 + c2 × c2 + c2d2

[Using (2) and (3) and rearranging terms]

= a2(b2 + c2 + d2) + b2(b2 + c2 + d2) + c2(b2 + c2 + d2)

= (a2 + b2 + c2) (b2 + c2 + d2)

= L.H.S

L.H.S. = R.H.S

(a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2

Solution 26

Solution 27

Solution 28


Solution 29


Solution 30

Solution 31

Solution 32

Sequences and Series Exercise Misc. Ex.

Solution 1

Solution 2

Solution 3

Solution 4


Solution 5

Solution 6

Solution 7

Solution 8

Solution 9



Solution 10


Solution 11


Solution 12

Solution 13


Solution 14


Solution 15

Solution 16

Solution 17

Solution 18


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