What is \sum_{x=1}^{5}f(2x-1) 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. 341
- B. 682 ✓
- C. 1023
- D. 1364
Correct Answer: B. 682
Explanation
Since f(x) = 2^x, we have f(2x-1) = 2^{2x-1}. Expanding the sum for x=1 to 5 gives 2^1 + 2^3 + 2^5 + 2^7 + 2^9 = 2 + 8 + 32 + 128 + 512 = 682.
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