Without doing actual addition, find the sum of:
$1 + 3 + 5 + 7 + 9 + \dots + 51 + 53$

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Solution

$We know that the sum of first n odd numbers is given by n^{2} .$
$Here, n = 27$
$So, 1 + 3 + 5 + 7 + 9 + \dots + 51 + 53 = 272 = 729$

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Without doing te actual addition, find the sum of :

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

(ii) 1+3+5+7+9+....... +39+41

(iii) 1+3+5+7+9+........+51+53

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15.

Find the sum 1 + 3 + 5 + … + 51 (the sum of all odd numbers from 1 to 51) without actually adding them.

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