Without adding find the sum - \(1 + 3 + 5 + 7 + 9\)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\)
- \(1 + 3 + 5 + 7 + 9\)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 \)
- \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23\)
Solution and Explanation
We know that the sum of first n odd natural numbers is \(n^2\).
(i) Here, we have to find the sum of first five odd natural numbers.
Therefore, \(1 + 3 + 5 + 7 + 9 = (5)^2= 25\)
(ii) Here, we have to find the sum of first ten odd natural numbers.
Therefore, \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = (10)^2= 100\)
(iii) Here, we have to find the sum of first twelve odd natural numbers.
Therefore, \(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19 + 21 + 23 = (12)^2= 144\)
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