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Question

Find the value of
(i) 1 + 3 + 5 = _____
(ii) 1 + 3 + 5 + 7 + 9 +11 = ________
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 =_____

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Solution

Sum of n consecutive odd integers starting from 1 is equal to n2
(i) 1+3+5=32=9
(ii) 1+3+5+7+9+11=62=36
(iii) Sum of n consecutive odd integers starting from 1 is equal to n2
Here the total number of consecutive odd integers is 9.
Thus, n = 9 and their sum is 92=81.
(In fact: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81)

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