Question

without adding find the sum 1 + 3 + 5 + 7 + _______________+23​

Answer 1

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Answer 2

Answer:

The answer is - 144

Step-by-step explanation:

To find the sum without actually adding the numbers

So,

= 1 + 3 + 5 + 7 + ..................  + 23

means

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23(12 numbers to be added)

Sum without actually adding the numbers [Trick]

As there are 12 numbers so the sum of the numbers is $12^{2}$ = 144

The trick is that when the odd numbers are been added from the starting, so the sum is the square of the amount of the numbers.