Question

Answer 1

\(a,S=1-2+3-4+5-6+...+2021-2022+2023\\ =\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+...+\left(2021-2022\right)+2023\\ =\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)+2023\\ =\left(-1\right).1011+2023\\ =\left(-1011\right)+2023\\ =3034\)

\(b,T=1-4+7-10+...+307-310+313\\ =\left(1-4\right)+\left(7-10\right)+...+\left(307-310\right)+313\\ =\left(-3\right)+\left(-3\right)+...+\left(-3\right)+313\\ =\left(-3\right).52+313\\ =157\)

 

Answer 2

a: =(-1)+(-1)+...+(-1)+2023

=2023-1011=1012

b: =(-3)+(-3)+...+(-3)+313

=313-3*52

=157