35/172

\(\left(\frac{99^9}{11^9}-\frac{99^{99}}{11^{99}}-\frac{99^{999}}{11^{999}}\right)\left(\frac{1}{5}-\frac{1}{7}-\frac{2}{35}\right)\)

\(=\left(\frac{99^9}{11^9}-\frac{99^{99}}{11^{99}}-\frac{99^{999}}{11^{999}}\right)\left(\frac{7}{35}-\frac{5}{35}-\frac{2}{35}\right)\)

\(=\left(\frac{99^9}{11^9}-\frac{99^{99}}{11^{99}}-\frac{99^{999}}{11^{999}}\right).0\)

\(=0\)

bài dễ thế không ai làm được hay thật

\(B=\frac{1}{3}-\frac{3}{4}+0,6+\frac{1}{64}-\frac{2}{9}-\frac{1}{36}+\frac{1}{15}\)

\(\Rightarrow B=\frac{3}{15}-\frac{48}{64}+\frac{9}{15}+\frac{1}{64}-\frac{8}{36}-\frac{1}{36}+\frac{1}{15}\)

\(\Rightarrow B=\frac{3}{15}+\frac{9}{15}+\frac{1}{15}+\left(-\frac{48}{64}+\frac{1}{64}\right)+\left(-\frac{8}{36}-\frac{1}{36}\right)\)

\(\Rightarrow B=\frac{13}{15}-\frac{47}{64}-\frac{1}{4}\)

\(\Rightarrow B=-\frac{113}{960}\)

\(C=0\)

\(D=\frac{1}{99}-\frac{1}{99.98}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(\Rightarrow D=\frac{1}{99}-\frac{1}{99}+\frac{1}{98}-\frac{1}{98}+...-\frac{1}{3}+\frac{1}{2}-\frac{1}{2}+1\)

\(\Rightarrow D=1\)

D= \(\frac{1}{99}-\frac{1}{99.98}-\frac{1}{98.97}......-\frac{1}{3.2}-\frac{1}{2.1}\)

=\(\frac{1}{99}-\left(\frac{1}{1.2}+\frac{1}{2.3}+.......+\frac{1}{97.98}+\frac{1}{98.99}\right)\)

=\(\frac{1}{99}-\left(1-\frac{1}{2}+\frac{1}{2}-.....-\frac{1}{98}-\frac{1}{99}\right)\)

=\(\frac{1}{99}-\left[1-(\frac{1}{2}-\frac{1}{2}+......+\frac{1}{98}-\frac{1}{99})\right]\)

=\(\frac{1}{99}-\left(1-0-0-.....-0-\frac{1}{99}\right)\)

=\(\frac{1}{99}-1-\frac{1}{99}\)

=1

\(a)\frac{-3}{4}+\frac{3}{7}+-\frac{1}{4}+\frac{4}{9}+\frac{4}{7}\)

\(=\left(\frac{-3}{4}+-\frac{1}{4}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\frac{4}{9}\)

\(=-1+1+\frac{4}{9}\)

\(=\frac{4}{9}\)

\(\frac{-3}{4}+\frac{3}{7}+\frac{-1}{4}+\frac{4}{9}+\frac{4}{7}\)

\(=\left(\frac{-3}{4}+\frac{-1}{4}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)+\frac{4}{9}\)

\(=\left(-1\right)+1+\frac{4}{9}\)

\(=0+\frac{4}{9}\)

\(=\frac{4}{9}\)

GIÚP MIK IK XIN CÁC BN ĐÓ

= 1/3 - 1/3 + 5/7 - 5/7 - 7/9 + 7/9 +9/11 - 9/11 -11/13 + 11/13 +13/15

= 0 + 0 - 0 + 0 -0 + 13/15

= 0 + 13/15

= 13/15

\(\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{13}{15}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)

\(=\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{3}{5}-\frac{3}{5}\right)+\left(\frac{5}{7}-\frac{5}{7}\right)+\left(\frac{7}{9}-\frac{7}{9}\right)+\left(\frac{9}{11}-\frac{9}{11}\right)+\left(\frac{11}{13}-\frac{11}{13}\right)+\frac{13}{15}\)

\(=0+0+0+0+0+0+\frac{13}{15}\)

\(=\frac{13}{15}\)

\(S=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{99.101}\right)=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-...-\frac{1}{101}\right)=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{101}\right)\)

\(=\frac{3}{2}.\frac{96}{505}=\frac{288}{1010}\)

\(S=\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{99.101}\)

\(\Rightarrow S=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\right)\)

\(\Rightarrow S=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(\Rightarrow S=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{101}\right)=\frac{3}{2}.\frac{96}{505}\)

\(\Rightarrow S=\frac{144}{505}\)

S = \(\frac{3}{5\times7}+\frac{3}{7\times9}+\frac{3}{9\times11}+..+\frac{3}{99\times101}\)

=\(\frac{3}{5}-\frac{3}{7}+\frac{3}{7}-\frac{3}{9}+...+\frac{3}{99}-\frac{3}{101}\)(Công thức là thế !)

=\(\frac{3}{5}-\frac{3}{101}\)

=\(3\times\left(\frac{1}{5}-\frac{1}{101}\right)\)

=3\(\times\frac{96}{505}\)

=\(\frac{288}{505}\)

= -59/105

k mình nha

k mình nha

dài quá! mình bó tay luôn!