Functions
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MMTS_Full_Test_07
Grade 12
Question:
If $f(x+y)=f(x)\cdot f(y)$ for all $x,y$ and $f(1)=2$, then $\sum_{k=1}^n f(k)=$
$2(2^n-1)$
$2^{n+1}-2$
$2^n-1$
$2^{n+1}$
Step-by-Step Solution
Key Concept: $f(k)=f(1)^k=2^k$; sum geometric series
$2+4+\cdots+2^n=2(2^n-1)=2^{n+1}-2$.
Correct Answer: 1