Q.

Without adding, find the sum.

(i) 1 + 3 + 5 + 7 + 9 

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

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Detailed Solution

Without adding the numbers the sum of the given numbers are as follows : 

(i) 1 + 3 + 5 + 7 + 9 

There are total 5  consecutive odd numbers

Therefore, the sum of given numbers = 52 = 25

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19

There are total 10 consecutive odd numbers

Therefore, the sum of given numbers = 102 = 100

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

There are total 12 consecutive odd numbers

Therefore, the sum of given numbers =122 = 144

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