NCERT Class 11 Mathematics Solutions: Chapter 9 –Sequences and Series Miscellaneous Exercise 9 Part 9
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Sum of a Geometric Series
Sum of a Geometric Series
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