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If Sp denotes the sum of the series 1+r^...

If `S_p` denotes the sum of the series `1+r^p+r^(2p)+ toooa n ds_p` the sum of the series `1-r^(2p)r^(3p)+ tooo,|r|<1,t h e nS_p+s_p` in term of `S_(2p)` is `2S_(2p)` b. `0` c. `1/2S_(2p)` d. `-1/2S_(2p)`

A

`2S_(2p)`

B

0

C

`1/2S_(2p)`

D

`-1/2S_(2p)`

Text Solution

Verified by Experts

The correct Answer is:
A
`S_(p)=1/(1-r^(P)),s_(P)=1/(1+r^(p)),S_(2p)=1/(1-r^(2p))`
Clearly
`S_(p)+s_(p)=2/(1-r^(2p))=2S_(2p)`
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