Calculators are not allowed

Algebra Level 2

1 2 − 2 2 + 3 2 − 4 2 + 5 2 − 6 2 + . . . − 201 8 2 + 201 9 2 = ? 1^2-2^2+3^2-4^2+5^2-6^2+...-2018^2+2019^2=?


The answer is 2039190.

The Sicilian Magician by The Sicilian Magician , 31, Italy

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1 solution

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Aug 15, 2018

1 2 − 2 2 + 3 2 − 4 2 + 5 2 − 6 2 + . . . − 201 8 2 + 201 9 2 1^2-2^2+3^2-4^2+5^2-6^2+...-2018^2+2019^2

= 1 + ( 3 + 2 ) ( 3 − 2 ) + ( 5 + 4 ) ( 5 − 4 ) + . . . + ( 2019 + 2018 ) ( 2019 − 2018 ) =1+(3+2)(3-2)+(5+4)(5-4)+...+(2019+2018)(2019-2018)

= 1 + 2 + 3 + 4 + 5 + . . . + 2018 + 2019 =1+2+3+4+5+...+2018+2019

= 2019 × 2020 2 =\dfrac{2019\times2020}{2}

= 2039190 =2039190

Actually,I used a calculator for the last step :p

2 Helpful 0 Interesting 0 Brilliant 0 Confused

I solved the same and used the calculator for the last step too which is ok, maybe.

Hana Wehbi - 2 years, 9 months ago

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