
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.


\(\frac{1+2+3+4+5+6+7+8+9.0}{1+2+3+4+5+6+7+8+9.0}\)
= 1
( Vì tử và mẫu đều giống nhau )

Đặt P = ... ( biểu thức đề bài )
Nhận xét: Với \(k\inℕ^∗\) ta có:
\(\frac{k+2}{k!+\left(k+1\right)!+\left(k+2\right)!}=\frac{k+2}{k!+\left(k+1\right).k!+\left(k+2\right).k!}=\frac{k+2}{2.k!\left(k+2\right)}=\frac{1}{2.k!}\)
\(\Rightarrow\)\(P=\frac{1}{2.1!}+\frac{1}{2.2!}+...+\frac{1}{2.6!}=\frac{1}{2}\left(1+\frac{1}{2}+...+\frac{1}{720}\right)=...\)

bài 1b)
\(8\frac{1}{14}-6\frac37\)
C1:\(\frac{113}{14}-\frac{45}{7}\) =\(\frac{113}{14}-\frac{90}{14}=\frac{23}{14}\)
C2:\(8\frac{1}{14}-6\frac37=\left(8-6\right)+\left(\frac{1}{14}-\frac37\right)=2+\left(\frac{1}{14}-\frac{6}{14}\right)\)
\(=2+\frac{-5}{14}=\frac{28}{14}-\frac{5}{14}=\frac{23}{14}\)
bài 1 c)\(7-3\frac67\)
C1:\(\) \(7-3\frac67=7-\frac{27}{7}=\frac{49}{7}-\frac{27}{7}=\frac{22}{7}\)
C2:\(7-3\frac67=\left(7-3\right)-\frac67=4-\frac67=\frac{28}{7}-\frac67=\frac{22}{7}\)

A=1−3+5−7+...+2001−2003+2005S=1−3+5−7+...+2001−2003+2005
=(1−3)+(5−7)+...+(2001−2003)+2005=(1−3)+(5−7)+...+(2001−2003)+2005(Có 1002 cặp)
=(−2).1002+2005=(−2).1002+2005
=−2004+2005=−2004+2005
=1

a)\(\frac{\frac{51}{2}}{\frac{13}{2}}\)=\(\frac{51}{13}\)
b)\(-\frac{5}{\frac{15}{32}}:\frac{\frac{23}{52}}{\frac{8}{3}}=-\frac{13312}{207}\)

\(4\frac{5}{6}+\frac{1}{6}.\left(8-2\frac{2}{3}\right)\)
\(=\frac{29}{6}+\frac{1}{6}.\left(8-\frac{8}{3}\right)\)
\(=\frac{29}{6}+\frac{1}{6}.\left(\frac{24}{3}-\frac{8}{3}\right)\)
\(=\frac{29}{6}+\frac{1}{6}.\frac{16}{3}\)
\(=\frac{29}{6}+\frac{8}{9}\)
=\(=\frac{103}{18}\)
\(4\frac{5}{6}+\frac{1}{6}.\left(8-2\frac{2}{3}\right)\)
\(=\frac{29}{6}+\frac{1}{6}.\left(8-\frac{8}{3}\right)\)
\(=\frac{29}{6}+\frac{1}{6}.\left(\frac{24}{3}-\frac{8}{3}\right)\)
\(=\frac{29}{6}+\frac{1}{6}.\frac{16}{3}\)
\(=\frac{29}{6}+\frac{8}{9}\)
\(=\frac{87}{18}+\frac{16}{18}\)
\(=\frac{103}{18}\)
1150