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If 0ltaltb, then lim(nto oo) (a^(n)+b^(n...

If 0ltaltb, then `lim_(nto oo) (a^(n)+b^(n))/(a^(n)-b^(n))`

A

equals 0

B

equals -1

C

equals 1

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(nto oo)(lim)(a^(n)+b^(n))/(a^(n)-b^(n))`
`=underset(n to oo)(lim)(a^(n)+b^(n))/(a^(n)-b^(n))`
`=underset(nto oo)(lim)(((a)/(b))^(n)+1)/(((a)/(b))^(n)-1)=-1`
[Since, `0 lt (a)/(b) lt 1` implies `((a)/(b))^(n)to0` as `nto oo`]
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