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\(B=-\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-...-\frac{1}{98.99}-\frac{1}{99.100}\\
=-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\\
=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\\
=-\left(1-\frac{1}{100}\right)=\frac{-99}{100}\)
17 x 85 + 15 x 17 - 17
= 17 x (85 + 15) - 17
= 17 x 100 - 17
= 1700 - 17
= 1683
B=(\(\left(\dfrac{4}{9}+\dfrac{5}{9}\right).\left(\dfrac{-1}{19}\right)\)
=1.\(\dfrac{-1}{19}\)
=\(\dfrac{-1}{19}\)
=(-1/19)x(4/9+5/9)
\(A=13.15+15.17+17.19+...+99.101\)
\(\Rightarrow6A=13.15.6+15.17.6+17.19.6+...+99.101.6\)
\(\Rightarrow6A=13.15.\left(17-11\right)+15.17.\left(19-13\right)+17.19.\left(21-15\right)+...+99.101.\left(103-97\right)\)
\(\Rightarrow6A=\left(13.15.17-11.13.15\right)+\left(15.17.19-13.15.17\right)+\left(17.19.21-15.17.19\right)+...+\left(99.101.103-97.99.101\right)\)
\(\Rightarrow6A=99.101.103-11.13.15\)
\(\Rightarrow6A=1027752\)
\(\Rightarrow A=171292\)
