Eric Nicholas K's answer to ok's Junior College 1 H2 Maths Singapore question.
done
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clear
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Not 100% sure about this as I do not usually answer JC level questions.
Date Posted:
4 years ago
Answer and approach are correct.
But it would be clearer to show how the 2² is factored out for the second sum.
i.e along the lines of
-2 (2² + 4² + 6² + ... + (2n)² )
= -2 ( (1x2)² + (2x2)² + (3x2)² + ... + (2 x n)² )
= -2 (2²(1²) + 2²(2²) + 2²(3²) + ... + 2²n² )
= -2 (2²) (1² + 2² + 3² + ... + n²)
= -8 ∑(r = 1, to n terms) r²
But it would be clearer to show how the 2² is factored out for the second sum.
i.e along the lines of
-2 (2² + 4² + 6² + ... + (2n)² )
= -2 ( (1x2)² + (2x2)² + (3x2)² + ... + (2 x n)² )
= -2 (2²(1²) + 2²(2²) + 2²(3²) + ... + 2²n² )
= -2 (2²) (1² + 2² + 3² + ... + n²)
= -8 ∑(r = 1, to n terms) r²
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