But Exactly How Many Of Them?

Number Theory Level 3

Given that the sum of an even number of even numbers is always even. Analogously, can we say that the sum of an odd number of odd numbers is always odd?

No Yes

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Let the sum be ( 2 a 1 + 1 ) + ( 2 a 2 + 1 ) + ( 2 a 3 + 1 ) + … + ( 2 a 2 n − 1 + 1 ) (2a_1+1)+(2a_2+1)+(2a_3+1)+\ldots+(2a_{2n-1}+1) . This sum will be 2 ( a 1 + a 2 + a 3 + … + a 2 n − 1 ) + ( 2 n − 1 ) 2(a_1+a_2+a_3+\ldots+a_{2n-1})+(2n-1) which is odd.

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Great. For a fancier approach, we can solve this question by induction as well!

Pi Han Goh - 5 years, 1 month ago

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