MCQ
The arithmetic mean of $\{1, 2, 3, ..., n\}$ is :
- ✓$\frac{\text{n}+1}{2}$
- B$\frac{\text{n}-1}{2}$
- C$\frac{\text{n}}{2}$
- D$\frac{\text{n}}{2}+1$
✓
Answer
Correct option: A.
$\frac{\text{n}+1}{2}$
Arithmetic mean of $\{1, 2, 3, ......, n\}$
$=\frac{1+2+3+......+\text{n}}{\text{n}}$
$=\frac{\frac{\text{n}(\text{n}+1)}{2}}{\text{n}}$
$=\frac{\text{n}+1}{2}$
Hence, the correct option is $(a)$
$=\frac{1+2+3+......+\text{n}}{\text{n}}$
$=\frac{\frac{\text{n}(\text{n}+1)}{2}}{\text{n}}$
$=\frac{\text{n}+1}{2}$
Hence, the correct option is $(a)$
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