a)
\(A=1152-\left(374+1152\right)+\left(-65+374\right)\\ =\left(1152-1152\right)+\left(-374+374\right)-65\\ =-65\)
b)
\(B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+...+\dfrac{1}{96.101}\\ =\dfrac{1}{5}\left(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+...+\dfrac{5}{96.101}\right)\\ =\dfrac{1}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{96}-\dfrac{1}{101}\right)\\ =\dfrac{1}{5}\left(1-\dfrac{1}{101}\right)\\ =\dfrac{1}{5}.\dfrac{100}{101}=\dfrac{20}{101}\)
\(a,A=1152-\left(374+1152\right)+\left(-65+374\right)\)
\(A=1152-374-1152-65+374\)
\(A=\left(1152-1152\right)+\left(374-374\right)-65\)
\(A=0-0-65\)
\(A=-65\)
\(b,B=\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+...+\dfrac{1}{96.101}\)
\(B=\dfrac{1}{5}.\left(\dfrac{1}{1.6}+\dfrac{1}{6.11}+\dfrac{1}{11.16}+...+\dfrac{1}{96.101}\right)\)
\(B=\dfrac{1}{5}.\left(1-\dfrac{1}{6}+...+\dfrac{1}{96}-\dfrac{1}{101}\right)\)
\(B=\dfrac{1}{5}.\left(1-\dfrac{1}{101}\right)\)
\(B=\dfrac{1}{5}.\dfrac{100}{101}\)
\(B=\dfrac{20}{101}\)
