Ta có : 

\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{99^2}{99.100}\)

\(=\)\(\frac{1^2.2^2.3^2.....99^2}{1.2.2.3.3.4.....99.100}\)

\(=\)\(\frac{1^2.2^2.3^2.....99^2}{1^2.2^2.3^2.4^2.....99^2}.\frac{1}{100}\)

\(=\)\(\frac{1}{100}\)

Ta có: \(\frac{9}{21}=\frac{9:3}{21:3}=\frac{3}{7}\)

Và       \(\frac{-10}{15}=\frac{-10:5}{15:5}=-\frac{2}{3}\)

\(\Rightarrow\frac{9}{21}+\frac{-10}{15}=\frac{3}{7}+\frac{-2}{3}=\frac{9}{21}+\frac{-14}{21}=\frac{9+\left(-14\right)}{21}=\frac{-5}{21}\)

Tương tự: \(\frac{24}{56}=\frac{24:8}{56:8}=\frac{3}{7}\)

Và \(\frac{-18}{27}=\frac{-18:9}{27:9}=\frac{-2}{3}\)

\(\Rightarrow\frac{24}{56}+\frac{-18}{27}=\frac{3}{7}+\frac{-2}{3}=\frac{-5}{21}\)

\(\frac{3}{7}+\frac{-2}{3}=\frac{9}{21}-\frac{14}{21}=\frac{-5}{21}\)

\(\frac{9}{21}+\frac{-10}{15}=\frac{3}{7}-\frac{2}{3}=\frac{-5}{21}\)

\(\frac{24}{56}+\frac{-18}{27}=\frac{3}{7}-\frac{2}{3}=\frac{-5}{21}\)

\(\frac{-5}{12}+\frac{-1}{4}=\frac{-5}{12}+\frac{-3}{12}=\frac{-5+-3}{12}=\frac{-8}{12}=\frac{-2}{3}\)

\(\frac{5}{12}+\frac{-3}{28}=\frac{35}{84}+\frac{-9}{84}=\frac{35+\left(-9\right)}{84}=\frac{26}{84}=\frac{13}{42}\)

\(\frac{-7}{15}+\frac{3}{35}=\frac{-49}{105}+\frac{9}{105}=\frac{-49+9}{105}=\frac{-40}{105}=\frac{-8}{21}\)

\(\frac{-5}{7}+\frac{-3}{4}=\frac{-20}{28}+\frac{-21}{28}=\frac{-20+\left(-21\right)}{28}=\frac{-41}{28}\)

\(\frac{-24}{54}+\frac{35}{-126}=\frac{-4}{9}+\frac{-5}{18}=\frac{-8}{18}+\frac{-5}{18}=\frac{-8+-5}{18}=\frac{-13}{18}\)

\(-\frac{3}{27}+\frac{56}{88}=\frac{-1}{9}+\frac{7}{11}=\frac{-11}{99}+\frac{63}{99}=\frac{-11+63}{99}=\frac{52}{99}\)

13/5 + 5/3 = 64/15

-1/3 + 7/3 = 6/3

-7/2 + -3/4 =-17/4

\(\frac{13}{5}+\frac{5}{3}=\frac{39}{15}+\frac{25}{15}=\frac{64}{15}\)

\(\frac{-1}{3}+\frac{7}{3}=\frac{-1+7}{3}=\frac{6}{3}=2\)

\(\frac{-7}{2}+\frac{-3}{4}=\frac{-14}{4}+\frac{-3}{4}=\frac{-17}{4}\)

5 ( x + 6 ) = x ( 5 + 10 )

5x + 30 = 5x + 10x

5x - 5x - 10x = - 30

- 10x = - 30

x = - 30 : ( - 10 )

x = 3

\(5.\left(x+6\right)=x.\left(5+10\right)\)

\(\Rightarrow5x+30=15x\)

\(\Rightarrow5x-15x=-30\)

\(\Rightarrow-5x=-30\)

\(\Rightarrow x=6\)

Vậy x = 6

Tổng B có số số hạng là  (299-21)/1+1=279( số hạng)

Giá trị của tổng B là \(\frac{\left(299+21\right).279}{2}=44640\)

Vì 44640\(⋮\)3 nên B\(⋮\)3 (đpcm)