NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 9

Glide to success with Doorsteptutor material for UGC : fully solved questions with step-by-step explanation- practice your way to success.

Sum of a Geometric Series

Sum of a Geometric Series

Loading image

1. If are in G.P, prove that are in G.P.

Answer:

It is given that are in G.P.

……………………………eq (1)

……………………………eq (2)

…………………………… eq (3)

It has to be proved that are in G.P.

i.e

Consider L.H.S.

[Using (1) and (2)]

[Using (3)]

Thus, are in G.P.

2. If a and b are the roots of are roots of ,where , form a G.P.

Prove that .

Answer:

It is given that a and b are the roots of

…………………………eq (1)

Also, are the roots of

……………………… eq (2)

It is given that are in G.P.

Consider From (1) and (2), we obtain

On dividing, we obtain

When

When

Case I:

When ,

i.e.,

Case II

When ,

i.e.,

Thus, in both the cases, we obtain