Question

The value of \( {}^2P_1 + {}^3P_1 + \dots + {}^nP_1 \) is equal to:

• A. \( \frac{n^2 - n + 2}{2} \)
• B. \( \frac{n^2 + n + 2}{2} \)
• C. \( \frac{n^2 + n - 1}{2} \)
• D. \( \frac{n^2 - n - 1}{2} \)
• E. \( \frac{n^2 + n - 2}{2} \)

Hint:

If you forget the formula, test with $n=2$. The sum is just ${}^2P_1 = 2$. Plugging $n=2$ into option (E) gives $(4+2-2)/2 = 3

Answer 1

Answer: (E)