Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{1}{2}+\frac{2}{4}+\frac{3}{6}+\frac{4}{8}+\frac{5}{10}+\frac{6}{12}+\frac{7}{14}+\frac{8}{16}+\frac{9}{18}+\frac{10}{20}\)
\(=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
\(=\frac{1}{2}\times10\)
\(=\frac{10}{2}\)
\(=5\)
\(\frac{1}{2}\)+ \(\frac{2}{4}\)+ \(\frac{3}{6}\)+ \(\frac{4}{8}\)+ \(\frac{5}{10}\)+ \(\frac{6}{12}\)+ \(\frac{7}{14}\)+ \(\frac{8}{16}\)+ \(\frac{9}{18}\)+ \(\frac{10}{20}\)
= \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)+ \(\frac{1}{2}\)
= \(\frac{1}{2}\)x 10
= 5
khoảng cách: 2-1=1
số số hạng là: (20-1):1+1=20(số)
tổng là: (20+1)x20:2=210
tổng quát: \(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
Ta có: \(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{3}-\frac{1}{10}=\frac{10}{30}-\frac{3}{30}=\frac{7}{30}\)
\(\frac{2}{3}:\frac{5}{6}=\frac{4}{5}\)
\(\frac{4}{5}\cdot\frac{2}{3}=\frac{8}{15}\)
Vậy : \(\frac{2}{3}:\frac{5}{6}< \frac{4}{5}x\cdot\frac{2}{3}\)nên \(\frac{4}{5}< \frac{8}{15}\)
Mình làm câu A
\(\frac{1}{2}\cdot\frac{3}{4}=\frac{3}{8}\)\(;\frac{5}{8}:\frac{6}{8}=\frac{5}{6}\)
Vậy \(\frac{1}{2}\cdot\frac{3}{4}< \frac{5}{8}:\frac{6}{8}\)
Nên : \(\frac{3}{8}< \frac{5}{6}\)
\(\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{9\times10}+\frac{1}{10\times11}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
( gạch bỏ các phân số giống nhau )
\(=\frac{1}{3}-\frac{1}{11}\)
\(=\frac{8}{33}\)
CHÚC BN HỌC TỐT!!!
A.\(\frac{12}{15}>\frac{8}{15}\)
B.\(\frac{3}{8}< \frac{5}{6}\)
C.\(\frac{6}{7}< \frac{14}{3}\)
D.\(\frac{143}{144}>\frac{99}{100}\)
Nhớ k mình nha