Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Tính :
a) \(M=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}\)
\(=\frac{100}{101}\)
b) \(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)
\(=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(=7.\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(=7.\frac{3}{35}\)
\(=\frac{3}{5}\)
c) \(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)
\(=\frac{1}{2}.\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(=\frac{1}{2}.\frac{2}{75}\)
\(=\frac{1}{75}\)
a)100-9:(372:3.y-1)-14=83
<=>100-9:(124y-1)-14=83
<=>86-9:(124y-1)=83
<=>9:(124y-1)=3
<=>124y-1=3
<=>124y=4
<=>y=\(\frac{1}{31}\approx0,3223\)
b)7260-120:24.y+924=528,3
<=>8184-5y=528,3
<=>5y=7655,7
<=>y=1531,14
c)2000-52:(615:3:y-15)-14=1984
<=>1986-52:(205:y-15)=1984
<=>52:(205:y-15)=2
<=>205:y-15=26
<=>205:y=41
<=>y=5
d)y+y.1/3+5/18=7/18
<=>4/3y=1/9
<=>y=1/12
e)13/15-(5/21+y)7/12=7/10
<=>7/12.(5/21+y)=1/6
<=>5/36+7/12y=1/6
<=>7/12y=1/36
<=>y=1/21\(\approx\)0,4762
h)y+2.y+3.y+...+10.y=49,5
<=>55y=49,5
<=>y=0,9
i)y.(1975/8.9+1885/9.10+1755/10.11+1579/11.12)=1/24
<=>7991,364899y=1/24
<=>y=33/6329161
tích nha mỏi tay quá
A=1/1.2+1/2.3+1/3.4+..+1/99.100
=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
=1-1/100
=99/100
ko ghi lại đề
\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{210}-\frac{1}{211}+\frac{1}{211}-\frac{1}{212}\)
\(=1-\frac{1}{212}\)
\(=\frac{211}{212}\)
\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)
\(A=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+\frac{1}{\left(1+5\right).5:2}\)
\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{6}\right)\)
\(A=2.\frac{1}{3}=\frac{2}{3}\)
