Find the sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19, without performing each term addition.

100

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Solution

The correct option is A 100
Sum of first n odd numbers = n $^{2}$
Here there are 10 odd numbers.

Hence,
$1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 10^{2}$
$= 100$

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1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

1 + 3 + 5 + 7 + 9

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

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

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + . . . . + 33

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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1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

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

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