Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a,-3/5.2/7+-3/7.3/5+-3/7
=-3/7.2/5+(-3/7).3/5+(-3/7)
=-3/7(2/5+3/5+1)
=-3/7.2
=-6/7
\(A=-\frac{1}{20}+-\frac{1}{30}+-\frac{1}{42}+...+-\frac{1}{90}\)
\(\Leftrightarrow A=\left(-1\right)\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=\left(-1\right)\left(\frac{1}{4}-\frac{1}{10}\right)\)
\(A=-\frac{3}{20}\)
Bài 1: <Cho là câu a đi>:
a. \(\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{49}{50}\)
\(\rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{49}{50}\)
\(\rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{49}{50}\)
\(\rightarrow1-\frac{1}{x+1}=\frac{49}{50}\)
\(\rightarrow\frac{1}{x+1}=1-\frac{49}{50}=\frac{1}{50}\)
\(\rightarrow x+1=50\rightarrow x=49\)
Vậy x = 49.
\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{1000}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{999}{1000}\)
\(=\frac{1}{1000}\)
chúc
bn
hk
tốt

\(P=\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}=\left(\frac{4}{11}+\frac{3}{22}\right)+\left(\frac{5}{2}+\frac{1}{30}+\frac{13}{60}\right)=\frac{1}{2}+\frac{11}{4}=\frac{13}{4}\)
\(Q=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}=\frac{1.2.3....19}{2.3.4....20}=\frac{1}{20}\)
Cảm ơn mina-san nha! Mình đang tìm câu hỏi nào đáng tin cậy nhất rùi mới s
\(P=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(\Rightarrow P=\frac{1}{7}\left(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\right):\frac{1}{7}\)
\(\Rightarrow P=\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{2.15}+\frac{13}{15.28}\right):\frac{1}{7}\)
\(\Rightarrow P=\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right):\frac{1}{7}\)
\(\Rightarrow P=\left(\frac{1}{2}-\frac{1}{28}\right):\frac{1}{7}\)
\(\Rightarrow P=\left(\frac{14}{28}-\frac{1}{28}\right):\frac{1}{7}\)
\(\Rightarrow P=\frac{13}{28}:\frac{1}{7}\)
\(\Rightarrow P=\frac{13.7}{28}\)
\(\Rightarrow P=\frac{13}{4}\)
Tính giá trị biểu thức
P = \(\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
P = \(\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}\)
P = \((\frac{5}{2}+\frac{1}{30}+\frac{13}{60})+(\frac{4}{11}+\frac{3}{22})\)
P = \(\frac{11}{4}+\frac{1}{2}\)
P = \(\frac{13}{4}\)
Q = \((1-\frac{1}{2}).(1-\frac{1}{3}).(1-\frac{1}{4})...(1-\frac{1}{20})\)
Q = \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)
Q = \(\frac{1}{20}\)