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Question

Without adding, find the sum in the following:
(i) 1 + 3 + 5 + 7 + 9 +11+13
(ii) 1 + 3 + 5 + 7 + 9 +11+13+15+17+19+21+23+25+27+29+31

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Solution

(i) We know that the sum of first 'n' odd natural numbers is equal to <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> n2
Now first 7 odd natural numbers are added,
Therefore, 1 + 3 + 5 + 7 + 9 +11+13 = 72 = 49

(ii) We know that the sum of first 'n' odd natural numbers is equal to <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> n2
Now first 16 odd natural numbers are added,
Therefore, 1 + 3 + 5 + 7 + 9 +11+13+15+17+19+21+23+25+27+29+31 = 162 = 256


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