\(S=-\left(\dfrac{5-4}{4.5}+\dfrac{6-5}{5.6}+\dfrac{7-6}{6.7}+...+\dfrac{10-9}{9.10}\right)=\)

\(=-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)=\)

\(=-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)=-\dfrac{3}{20}\)

\(S=\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\\ S=\dfrac{-1}{4.5}+\dfrac{-1}{5.6}+\dfrac{-1}{6.7}+\dfrac{-1}{7.8}+\dfrac{-1}{8.9}+\dfrac{-1}{9.10}\\ S=-\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ S=-\left(\dfrac{1}{4}-\dfrac{1}{10}\right)=-\dfrac{3}{20}\)

Chúc học tốt!

= -3/12 :3 +17/36 = -1/4 . 1/3 +17/36 = -1/12 +17/36= -3/36 + 17/36 = 14/36 =7/18

\(B=\dfrac{2^2}{1.3}+\dfrac{2^2}{3.5}+\dfrac{2^2}{5.7}+...+\dfrac{2^2}{195.197}+\dfrac{2^2}{197.199}\)

\(\dfrac{B}{2}=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{195.197}+\dfrac{2}{197.199}\)

\(\dfrac{B}{2}=2-\dfrac{2}{3}+\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{5}-\dfrac{2}{7}+...+\dfrac{2}{195}-\dfrac{2}{197}+\dfrac{2}{197}-\dfrac{2}{199}\)

\(\dfrac{B}{2}=2-\dfrac{2}{199}=\dfrac{396}{199}\)

\(B=\dfrac{396}{199}.2=\dfrac{792}{199}\)

B=2^3(2^2/1-2^2/3+2^2/3-2^2/5+2^2/5-2^2/7+2^2/7...+2^2/195-2^2/197+2^2/197-2^2/199

B=2^3(2^2/1-2^2/199)

B=2^3(792/199)

B=6336/199

\(\dfrac{n-5}{n-3}=\dfrac{\left(n-3\right)-2}{n-3}=1-\dfrac{2}{n-3}\)

Để phân số nguyên thì n-3 phải là ước của 2

\(\Rightarrow n-3=\left\{-2;-1;1;2\right\}\Rightarrow n=\left\{1;2;4;5\right\}\)

cíu em vớiii

Ta có:1/2^2<1/1.2; 1/3^2<1/2.3;.....

=>1/2^2+1/3^2+1/4^2+1/5^2+...+1/100^2

<1/1.2+1/2.3+1/3.4+1/4.5+....+1/99.100(bạn ghi dấu "<" ở trên cũng được)

=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+....+1/99-1/100

=1/1-1/100=99/100

Mà 99/100<1

=>1/2^2+1/3^2+1/4^2+1/5^2+...+1/100^2<1