If f(x+y)=f(x)f(y) and Σₓ₌₁^∞ f(x)=2, x,y∈N where N is the set of all natural numbers, then the value of f(4)/f(2) is:
If f(x+y)=f(x)f(y) and Σₓ₌₁^∞ f(x)=2, x,y∈N where N is the set of all natural numbers, then the value of f(4)/f(2) is:
Option 1 -
2/3
Option 2 -
1/9
Option 3 -
1/3
Option 4 -
4/9
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:f (x+y)=f (x)f (y). f (n)=f (1)?
Σf (x)=f (1)/ (1-f (1)=2 ⇒ f (1)=2/3.
f (4)/f (2) = (f (1)? )/ (f (1)²) = f (1)² = 4/9.
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