\(A=\dfrac{5}{11}.\dfrac{5}{7}+\dfrac{5}{11}.\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}.1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=\dfrac{11}{11}=1\)

\(B=\dfrac{3}{13}.\dfrac{6}{11}+\dfrac{3}{13}.\dfrac{9}{11}-\dfrac{3}{13}.\dfrac{4}{11}=\dfrac{3}{13}\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}.1=\dfrac{3}{13}\)

\(C=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right).0=0\)

a. 

1+2+3+...+99+100

=(1+100)*100/2

=5050

b.12+14+16+...+38

=(12+38)*[(38-12)/2+1]/2

=350

a) 1 + 2 + 3 +... + 99 + 100 

= \(\left[\left(100-1\right):1+1\right]\times\frac{100+1}{2}\)

= \(100\times\frac{101}{2}\)

= \(5050\)

b) 12 +14 + 16 + ... + 36 + 38

= \(\left[\left(38-12\right):2+1\right]\times\frac{38+12}{2}\)

=\(14\times25\)

= \(350\)

a ) Vì dãy số đó có 100 số hạng

Tổng dãy số là

( 100 + 1 ) x 100 : 2 = 5050

b) Số số hạng dãy là

( 38 - 12 ) : 2 + 1 = 14 ( số )

Tổng dãy là

( 38 + 12 ) x 14 : 2 = 350

có một câu nữa : d)211/6 : (-4/5) - 271/6 : (-4/5)

a)13/2     b)9,925  c)-1  d)

a) 105*x-20-18-16-...-2=19+17+15+...+3+1

105*x=1+2+3+4+...+20

105*x=\(\frac{\left(20+1\right)x20}{2}\)

105*x=210

x=2

Vậy x = 2

b) 1-6+11-16+21-26+...+91-96+101

=101-96+91-86+...+21-16+11-6+1

=(101-96)+(91-86)+...+(21-16)+(11-6)+1

=5+5+...+5+5+1                ( có (101-6):5+1);2=10 số 5)

=5x10+1=51

a)105xX-20-18-16-...-2=19+17+15+...+3+1

105xX-(20+18+16+...+2)=19+17+15+...+3+1

105xX-110=100

105xX=100+110

105xX=210

X=210:105

X=2