Question

(i) Express 81 as the sum of 9 odd numbers.

(ii) Express 100 as the sum of 10 odd numbers.​

Answer 1

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$\purple{\textbf{\underline{\underline{SOLUTION :-}}}}$

Given 81 can be written as 9² According to the property of perfect square, for any natural number n, we have sum of first n odd natural numbers=n² Expressing 81 as a sum of 9 odd numbers, we get81= (9)²

Here n=9

By applying the law 81 = (1+3+5+7+9+11+13+15+17)

Given 100 can be written as 10² According to the property of perfect square, for any natural number n, we have sum of first n odd natural numbers=n² Expressing 100 as a sum of 10 odd numbers, we get100 = (10)²

Here n=10

By applying the law 81 = (1+3+5+7+9+11+13+15+17+19)

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