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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Solution

Here, the quotient obtained upon dividing 51 by 2 is 25.

∴Number of terms = n = 25 + 1 = 26

∴ 1 + 3 + 5 + … + 51 = 26² = 676

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Similar questions

1 + 3 + 5 + . . . . . + 51

1

51

1 + 3 + 5 + 7 + 9 + \dots + 51 + 53

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

1 + 3 + 5 + 7

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

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