Question:
The sum of odd integers from 1 to 2001 is
The sum of odd integers from 1 to 2001 is
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Sum of first \( n \) odd numbers is always a perfect square.
Updated On: May 1, 2026
- \( (1121)^2 \)
- \( (1101)^2 \)
- \( (1001)^2 \)
- \( (1021)^2 \)
- \( (1011)^2 \)
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The Correct Option is C
Solution and Explanation
Concept:
Sum of first \( n \) odd numbers:
\[
1 + 3 + 5 + \cdots = n^2
\]
Step 1: Identify last odd number.
\[ 2001 = 2n -1 \Rightarrow n = 1001 \]
Step 2: Count total terms.
There are 1001 odd numbers.
Step 3: Apply formula.
\[ \text{Sum} = n^2 = (1001)^2 \]
Step 4: Expand if needed.
\[ (1001)^2 = 1002001 \]
Step 5: Final answer.
\[ (1001)^2 \]
Step 1: Identify last odd number.
\[ 2001 = 2n -1 \Rightarrow n = 1001 \]
Step 2: Count total terms.
There are 1001 odd numbers.
Step 3: Apply formula.
\[ \text{Sum} = n^2 = (1001)^2 \]
Step 4: Expand if needed.
\[ (1001)^2 = 1002001 \]
Step 5: Final answer.
\[ (1001)^2 \]
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