MCQ
The sum of first $n$ odd natural numbers is:
- A$2n + 1$
- ✓$n^2$
- C$n^2 - 1$
- D$n^2 + 1$
✓
Answer
Correct option: B.
$n^2$
B. $n^2$
Solution:
Sum of frist n odd natural numbers $=\sum(2\text{n}-1)=2\sum\text{n}-\text{n}$
$=\frac{2\times\text{n}(\text{n}+1)}{2}-\text{n}=\text{n}(\text{n}+1)-\text{n}$
$=\text{n}^2+\text{n}-\text{n}=\text{n}^2$
Solution:
Sum of frist n odd natural numbers $=\sum(2\text{n}-1)=2\sum\text{n}-\text{n}$
$=\frac{2\times\text{n}(\text{n}+1)}{2}-\text{n}=\text{n}(\text{n}+1)-\text{n}$
$=\text{n}^2+\text{n}-\text{n}=\text{n}^2$
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