What is \sum_{x=1}^{6}2^{x}f(x) equal to?
Consider the following for the next three (03) items that follow : Let f(x) be a function satisfying f(x+y)=f(x)f(y) for <strong>ALL</strong> x, y\in N such that f(1)=2 :
- A. 1365
- B. 2730
- C. 4024
- D. 5460 ✓
Correct Answer: D. 5460
Explanation
Given f(x) = 2^x, the term inside the sum is 2^x f(x) = 2^x 2^x = 4^x. The sum is \sum_{x=1}^{6}4^x = 4^1 + 4^2 + \dots + 4^6. Using the sum of a GP: 4\frac{4^6-1}{4-1} = 4 \times \frac{4096-1}{3} = 4 \times 1365 = 5460.
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