Đặt \(A=\frac{1}{4.9}+\frac{1}{9.14}+...+\frac{1}{44.49}\)

\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{44}-\frac{1}{49}\)

\(5A=\frac{1}{4}-\frac{1}{49}\)

\(A=\frac{45}{196}:5=\frac{9}{196}\)

Đặt \(B=\frac{1-3-...-49}{89}\)

\(B=\frac{\left(1-3\right)-\left(5-7\right)-...-\left(47-49\right)}{89}\)

\(B=\frac{\left(-2\right)-\left(-2\right)-...-\left(-2\right)}{89}\)

\(B=\frac{-2+2+...+2}{89}\)

\(B=\frac{\left(-2\right)+2\times24}{89}\)

\(B=\frac{46}{89}\)

\(P=A.B=\frac{9}{196}.\frac{46}{89}\)

\(P=\frac{207}{8722}\)

Hỏi thật không

k thì sao

trả lời z cx nói

mình nghĩ là đề như vậy:

\(\frac{24}{8.16}-\frac{40}{16.24}+\frac{56}{24.32}-\frac{72}{32.40}=\frac{8+16}{8.16}-\frac{16+24}{16.24}+\frac{24+32}{24.32}-\frac{32+40}{32.40}\)

\(=\frac{8}{8.16}+\frac{16}{8.16}-\frac{16}{16.24}-\frac{24}{16.24}+\frac{24}{24.32}+\frac{32}{24.32}-\frac{32}{32.40}-\frac{40}{32.40}\)

\(=\frac{1}{16}+\frac{1}{8}-\frac{1}{24}-\frac{1}{16}+\frac{1}{32}+\frac{1}{24}-\frac{1}{40}-\frac{1}{32}\)

\(=\frac{1}{8}-\frac{1}{40}=\frac{1}{10}\)

Đặt \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{21.22}\)

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{21}-\frac{1}{22}\)

\(A=\frac{1}{5}-\frac{1}{22}\)

\(A=\frac{17}{110}\)

\(\frac{1}{5.6}\)+\(\frac{1}{6.7}\)+...+\(\frac{1}{21.22}\)

=\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)+...+\(\frac{1}{21}\)-\(\frac{1}{22}\)

=\(\frac{1}{5}\)-\(\frac{1}{22}\)

=\(\frac{17}{110}\)

\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{21}-\frac{1}{22}\)

\(A=\frac{1}{5}-\frac{1}{22}\)

\(A=\frac{22}{110}-\frac{5}{110}\)

\(A=\frac{17}{110}\)

Đặt biểu thức là A, ta có:

\(\frac{1}{7}A=\frac{5}{2.7}+\frac{4}{7.11}+\frac{2}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)

\(\frac{1}{7}A=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{15}-\frac{1}{28}\)

1/7 A = 1/2 - 1/28

1/7A = 17/28

=> A = 17/4

\(A=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{44\cdot49}\right)\frac{1-3-5-7-...-49}{89}\\ A=\frac{1}{5}\left(\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+\frac{5}{14\cdot19}+...+\frac{5}{44\cdot49}\right)\frac{1-\left(3+5+7+...+49\right)}{89}\\ A=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{44}-\frac{1}{49}\right)\frac{1-\frac{\left(49+3\right)\cdot24}{2}}{89}\\ A=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{49}\right)\cdot\left(-7\right)\\ A=\frac{1}{5}\cdot\frac{45}{196}\cdot\left(-7\right)\\ A=\frac{-9}{28}\)

1/13. 8/13 - 14/13 + 5/13 .1/13

= 1/13. ( 8/13+5/13) -14/13

= 1/13. 13/13-14/13

= 1/13 . 1 - 14/13

= 1/13-14/13

= -13/13

= -1

k cho mik nhoa

1/13. 8/13 - 14/13 + 5/13 .1/13

= 1/13. ( 8/13+5/13) -14/13

= 1/13. 13/13-14/13

= 1/13 . 1 - 14/13

= 1/13-14/13

= -13/13

= -1