Question
Asked Oct 24, 2019
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What is the units' digit of the sum of the squares of the first 2019 odd positive integers?

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Expert Answer

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Step 1

To find the sum of squares of the first 2019 odd positive integers.

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Odd Sum (Sum of square of all 2n numbers) - (Sum of square of first n even numbers) 2n*(2n+1) (2 2n+1) 2n(n+1)(2n+1) 6 2n*(2n+1) [(2* 2n 1) 2(n 1)] 6 2n*(2n+1) [4n1 2(n 1)] 6 n*(2n+ 1) [4n1 2n-2] n*(2n+1) [2n 1] n*(2n+1) (2n-1)

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Step 2

Now, to find the number of odd numbers until 2019.

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2n 1 2019 2n 2019 1 2n 2020 n 1010

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Step 3

To substitute the value of n as 1...

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Tagged in

Math

Algebra

Equations and In-equations