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Mathematics

Without doing the actual addition, find the sum of:

1 + 3 + 5 + 7 + 9 + …………… + 51 + 53

Sq & Sq Roots

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Answer

As we know that, the sum of first n odd natural numbers = n2.

1+3+5+9+...............+51+53=272=7291 + 3 + 5 + 9 + …………… + 51 + 53\\[1em] = 27^2\\[1em] = 729

Hence, 1 + 3 + 5 + 7 + 9 + …………… + 51 + 53 = 729.

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