If $$A=1+ra+r2a+r3a+$$…∞ and If $$B=1+rb+r2b+r3b+$$…∞,then ab is equal to

Correct option is 3logB−1B⁡A−1A

Questions

If $A = 1 + r^{a} + r^{2 a} + r^{3 a} + \dots \infty$ and If $B = 1 + r^{b} + r^{2 b} + r^{3 b} + \dots \infty,$ then $\frac{a}{b}$ is equal to

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logB⁡A

log1−B⁡(1−A)

logB−1B⁡A−1A

None of these

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detailed solution

Correct option is C

A=11−ra⇒1−ra=1A⇒ra=1−1A=A−1AB=11−rb⇒1−rb=1B⇒rb=1−1B=B−1B∴ alog⁡r=log⁡A−1A and blog⁡r=log⁡B−1Bab=log⁡A−1Alog⁡B−1B=logB−1B⁡A−1A

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If A=1+ra+r2a+r3a+…∞ and If B=1+rb+r2b+r3b+…∞,then ab is equal to

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Ready to Test Your Skills?

free study material

If $A = 1 + r^{a} + r^{2 a} + r^{3 a} + \dots \infty$ and If $B = 1 + r^{b} + r^{2 b} + r^{3 b} + \dots \infty,$ then $\frac{a}{b}$ is equal to