Question

Tính nhanh

201822- 201722+ 201622-201522+...+222-1

Answer 1

\(2018-2017+2016-2015+...+2-1\)(2018 số hạng)

\(=1+1+...+1\) (1009 số hạng)

\(=1\cdot1009\)

\(=1009\)

Answer 2

\(2018-2017+2016-2015+........+2-1\)

\(=\left(2018+2016+.........+2\right)-\left(2017+2015+.........+1\right)\)

\(=\dfrac{\left[\left(2018-2\right):2+1\right]\left(2018+2\right)}{2}-\dfrac{\left[\left(2017-1\right):2+1\right]\left(2017+1\right)}{2}\)

\(=1019090-1018081\)

\(=1009\)

Answer 3

\(2018-2017+2016-2015+...+2-1\)

=1+1+1+...+1(co1009 số 1)

=1009