Question

 

Answer 1

a: \(1-2+3-4+5-6+...+221-222\)

=(1-2)+(3-4)+(5-6)+...+(221-222)

=(-1)+(-1)+...+(-1)

\(=-1\cdot\dfrac{222}{2}=-111\)

b: \(1-6+2-7+...+55-60\)

=(1-6)+(2-7)+...+(55-60)

=(-5)+(-5)+...+(-5)

\(=-5\cdot55=-275\)

c: \(-1+2-3+4-5+6-...-1021+1022\)

\(=\left(-1+2\right)+\left(-3+4\right)+\left(-5+6\right)+...+\left(-1021+1022\right)\)

=1+1+...+1

\(=1\cdot\dfrac{1022}{2}=511\)

d: \(1-4+2-5+3-6+...+397-400\)

\(=\left(1-4\right)+\left(2-5\right)+\left(3-6\right)+...+\left(397-400\right)\)

\(=\left(-3\right)+\left(-3\right)+...+\left(-3\right)\)

\(=-3\cdot397=-1191\)

e: -10-20-...-150-160

\(=-10\left(1+2+...+16\right)\)

\(=-10\cdot\dfrac{16\cdot17}{2}=-5\cdot16\cdot17=-80\cdot17=-1360\)