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\(20^2-19^2+18^2-17^2+...+2^2-1^2\)
\(=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...\left(2-1\right)\left(2+1\right)\)
\(=39+35...+3\)
Đến đây ok r nhá
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\(\left(-1\right)^2+2^2-3^2+4^2-...-17^2+18^2-19^2+20^2\\ =\left(2^2-3^2\right)+\left(4^2-5^2\right)+...+\left(16^2-17^2\right)+\left(18^2-19^2\right)+\left(20^2-1^2\right)\\ =\left(2-3\right)\left(2+3\right)+\left(4-5\right)\left(4+5\right)+...+\left(16-17\right)\left(16+17\right)+\left(18-19\right)\left(18+19\right)+\left(20-1\right)\left(20+1\right)\\ =\left(-1\right)\cdot5+\left(-1\right)\cdot9+...+\left(-1\right)\cdot33+\left(-1\right)\cdot37+19\cdot21\\ =\left(-1\right)\left(5+9+...+33+37\right)+399\\ =\left(-1\right)\cdot189+399\\ =-189+399\\ =210\)
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\(\left(20^2+18^2+16^2+......+4^2+2^2\right)-\left(19^2+17^2+.....+3^2+1^2\right)\)
\(=20^2-19^2+18^2-17^2+......+2^2-1^2\)
\(=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+.......+\left(2-1\right)\left(2+1\right)\)
\(=39+35+....+7+3\)
\(=\left(39+3\right)\left[\left(39-3\right):4+1\right]:2=210\)
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