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Let f be a real valued function satisfyi...

Let f be a real valued function satisfying
` f(x+y)=f(x)f(y)` for all ` x, y in R ` such that `f(1)=2 `.
Then , `sum_(k=1)^(n) f(k)=`

A

`2^(n+1)-2`

B

`2^(n+1)-1`

C

`2^(n)-1)`

D

`2^(n)-2`

Text Solution

Verified by Experts

The correct Answer is:
A
We have , `f(x)=[f(1)]^(x)=2^(x)` for all ` x, y in R . `
`:. sum_(k=1)^(n)f(k)=sum_(k=1)^(n)2^(k)=2((2^(n)-1)/(2-1))=2x^(n+1)-2`
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