Question

100-99+98-97+96-95+...+8-7+6-5+4-3+2-1

Answer 1

`x=100-99+98-97+96-95+...+8-7+6-5+4-3+2-1=\\\\=1+1+1+...+1+1+1+1=1\cdot n=n\\\\and\ \ \ 2=100-2\cdot(n-1)\ \ \ \Rightarrow\ \ \ 2n=100\ /:2\ \ \ \Rightarrow\ \ \ n=50\\\\x=50`

Answer 2

`100-99+98-97+96-95+...+8-7+6-5+4-3+2-1\\\\=(100-99)+(98-97)+(96-95)+...+(4-3)+(2-1)\\\\=\underbrace{1+1+1+...+1}_(50)=\fbox{50}`