1+1/2.2.3/2+1/3.3.4/2+...........+1/20.20.21/2

=1+24.19/2=229

=1+1/2.(3.2/2)+1/3.(4.3/2)+1/4.(5.4/2)+...+1/20.(21.20/2)

=1+3/2+2+5/2+...+21/2 ( rút gọn)

=2/2+3/2+4/2+5/2+...+21/2

=(2+3+4+5+...+21)/2=(20.23)/2.2=(20.23)/4

=23.5=115

Ko bt mk lm dung ko nx?

a)\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{5\cdot6}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(=\left(1-\frac{1}{6}\right)+\left(\frac{1}{2}-\frac{1}{2}\right)+...+\left(\frac{1}{5}-\frac{1}{5}\right)\)

\(=\left(1-\frac{1}{6}\right)+0+...+0=1-\frac{1}{6}=\frac{6}{6}-\frac{1}{6}=\frac{5}{6}\)

b)\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)

\(=\left(\frac{1}{2}-\frac{1}{14}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+\left(\frac{1}{11}-\frac{1}{11}\right)\)

\(=\left(\frac{1}{2}-\frac{1}{14}\right)+0+...+0=\frac{1}{2}-\frac{1}{14}=\frac{7}{14}-\frac{1}{14}=\frac{6}{14}\)

Nhớ **** cho mình nhé bạn! chúc bạn học tốt

tick đúng cho mik nha please

\(A=\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)

\(A=\frac{2^{20}.2^{20}-2^{20}+3^{20}.2^{20}}{2^{20}.3^{20}-3^{20}+3^{20}.3^{20}}\)

\(A=\frac{\left(2^{20}-1+3^{20}\right).2^{20}}{\left(2^{20}-1+3^{20}\right).3^{20}}\)

\(\Rightarrow A=\frac{2^{20}}{3^{20}}\)

suy ra 

S=1+2+3+4+..+20

S=210

b:\(=\dfrac{3^3\cdot2^3+3\cdot2^2\cdot3^2+3^3}{-13}=\dfrac{3^3\left(2^3+2^2+1\right)}{-13}=-3^3=-27\)

a: \(=\dfrac{5^5\cdot4^5\cdot5^{10}}{10^{20}}=\dfrac{5^{15}\cdot2^{10}}{5^{20}\cdot2^{20}}=\dfrac{1}{5^5\cdot2^{10}}\)

b) \(\dfrac{6^3+3.6^2+3^3}{-13}=\dfrac{2^3.3^3+3.3^2.2^2+3^3}{-13}=\dfrac{3^3\left(2^3+2^2+1\right)}{-13}\)

\(=\dfrac{3^3.\left(8+4+1\right)}{-13}=\dfrac{3^3.13}{-13}=\dfrac{27}{-1}=-27\)

a)\(\dfrac{20^5.5^{10}}{100^5}=\dfrac{20^5.5^{10}}{20^5.5^5}=\dfrac{5^5}{1}=3125\)

A= 210

B= 116

C= 132

a.SSH : ( 20 - 1 ) : 1 + 1 = 20

    tổng  : (20 + 1 ) x 20 :2 = 210

b . SSH : (21 - 1) :2  +1 = 11

      tổng ; (21 + 1 ) x 11 : 2 = 121

c. SSH : ( 22 - 2 ) : 2 + 1 = 11

    tổng  : ( 22 + 2) x 11 : 2 = 132

A=1+2+3+...+20

=(20-1) : 1+1

=20

Tổng là (20+1)x20:2=210

B=1+3+5+...+21

=(21-1) : 2+1

=11

Tổng là (21+1)x11:2=121

C=2+4+6+...+22

=(22-2) :2+1

=11

Tổng là : (22+2) x11:2=132