M= 4^0-5^2-6^2-7^2-...-120^2

M=1-(5^2-6^2-7^2-...-120^2)

M=...

m = 2/3.5 + 2/5.7 + 2/7.9 + .... + 2/97.99

m= 1/3 - 1/5 + 1/5 - 1/7 + 1/95 - 1/97 + 1/97 - 1/99

m = 1/3 - 1/99

m = 32/99

M= \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) + \(\frac{2}{7.9}\) + ... + \(\frac{2}{97.99}\)

M= \(\frac{1}{3}\) - \(\frac{1}{5}\) + \(\frac{1}{5}\) - \(\frac{1}{7}\) + \(\frac{1}{7}\) - \(\frac{1}{9}\)+ ...+\(\frac{1}{97}\) - \(\frac{1}{99}\)

M= \(\frac{1}{3}\) - \(\frac{1}{99}\)

M=\(\frac{32}{99}\)

 k cho mình nha!

Ta có :

\(M=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\)

\(=1.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{97.99}\right)\)

\(=1.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{97}-\frac{1}{99}\right)\)

\(=1.\left(\frac{1}{3}-\frac{1}{99}\right)\)

\(=1.\frac{32}{99}\)

\(=\frac{32}{99}\)

\(\frac{2.6.1}{33.24}=\frac{12.1}{33.2.12}=\frac{1}{66}\)

\(\frac{21.4}{9.7.5.3}=\frac{7.3.4}{9.5.7.3}=\frac{4}{45}\)

P/s: Hoq chắc ((:

B=4*13/9*3-4/3*40/9

B=4/3*13/9-4/3*40/9

B=4/3*(13/9-40/9)

B=4/3*(-27)/9

B=4*(-3)/9

B=-4

A=6/7 + 1/7.(2/7+5/7)

A=6/7 + 1/7.7/7=6/7+1/7.1

A=6/7+1/7=7/7=1

M=8/3*2/5*3/8*10*19/2

M=(8/3*3/8)*(2/5*10)*19/2

M=1*4*19/2

M=28

\(=\dfrac{2}{7}+\dfrac{12}{7}+4\times\dfrac{2}{7}-\dfrac{2}{7}\\ =\dfrac{2}{7}\times\left(1+4-1\right)+\dfrac{12}{7}\\ =\dfrac{2}{7}\times4+\dfrac{12}{7}\\ =\dfrac{8}{7}+\dfrac{12}{7}=\dfrac{12+8}{7}=\dfrac{20}{7}\)

\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{13\cdot15}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)

\(=\frac{1}{3}-\frac{1}{15}\)

\(=\frac{4}{15}\)

\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{13\cdot15}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{13}+\frac{1}{15}-\frac{1}{15}\)

\(=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)

\(\frac{2}{3.5}\)+ \(\frac{2}{5.7}\)+ \(\frac{2}{7.9}\)+...+ \(\frac{2}{13.15}\)= \(\frac{1}{3}\)- \(\frac{1}{5}\)+ \(\frac{1}{5}\)- \(\frac{1}{7}\)+ \(\frac{1}{7}\)- \(\frac{1}{9}\)+...+ \(\frac{1}{13}\)- \(\frac{1}{15}\)= \(\frac{1}{3}\)- \(\frac{1}{15}\)= \(\frac{4}{15}\).

4/9 x ( 5/7 + 2/5 + -2/7 + 7/5) 

Rồi sau đó bạn tự tính phần trong ngoặc ra(có thể sử dụng các tính chất của phân số để tính cho nhanh) rồi nhân với 4/9 là xong

Ta có: \(A=\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{99\cdot101}\)

\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(=\dfrac{1}{3}-\dfrac{1}{101}\)

\(=\dfrac{98}{303}\)

Với công thức \(\dfrac{a}{x.\left(x+a\right)}=\dfrac{a}{x}-\dfrac{a}{x+a}\)

Ta có: \(A=\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{5}-\dfrac{2}{7}+...+\dfrac{2}{99}-\dfrac{2}{101}\)

\(=\dfrac{2}{3}-\dfrac{2}{101}\)