(1+2+3+..+2046)x(15x13-15x12-15)=(1+2+...+2046)x15x(13-12-1)=0

100km

cần lm hộ ko 

mà rem và rem sai xùi

kết quả là 6015

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(=\frac{1}{1}-\frac{1}{6}\)

\(=\frac{5}{6}\)

\(\frac{1}{1.2}\)\(+\)\(\frac{1}{2.3}\)\(+\)\(\frac{1}{3.4}\)\(+\)\(\frac{1}{4.5}\)\(+\)\(\frac{1}{5.6}\)

\(=\)\(\frac{1}{1}\)\(-\)\(\frac{1}{2}\)\(+\)\(\frac{1}{2}\)\(-\)\(\frac{1}{3}\)\(+\)\(\frac{1}{3}\)\(-\)\(\frac{1}{4}\)\(+\)\(\frac{1}{4}\)\(-\)\(\frac{1}{5}\)\(+\)\(\frac{1}{5}\)\(-\)\(\frac{1}{6}\)

\(=\)\(\frac{1}{1}\)\(-\)\(\frac{1}{6}\)

\(=\)\(\frac{5}{6}\)

Hok tốt

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 +...+ 1/14 - 1/15 + 1/15 - 1/16

= 1/4 - 1/16

= 3/16

Công thức : 1/ a x (a+1) = 1/a - 1/ a+1

a) \(\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{202.509}=\frac{2}{4.9}+\frac{2}{9.14}+\frac{2}{14.19}+...+\frac{2}{504.509}\)

\(=\frac{2}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)

\(=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{504}-\frac{1}{509}\right)=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{509}\right)\)

\(=\frac{2}{5}.\frac{505}{2036}=\frac{101}{1018}\)

b) \(\frac{1}{10.9}+\frac{1}{18.13}+...+\frac{1}{802.405}=\frac{2}{10.18}+\frac{2}{18.26}+...+\frac{2}{802.810}\)

\(=\frac{2}{8}\left(\frac{8}{10.18}+\frac{8}{18.26}+...+\frac{8}{802.810}\right)=\frac{1}{4}\left(\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+...+\frac{1}{802}-\frac{1}{810}\right)\)

\(=\frac{1}{4}\left(\frac{1}{10}-\frac{1}{810}\right)=\frac{1}{4}.\frac{40}{405}=\frac{10}{405}\)

Bạn vào câu hỏi tương tự tham khảo !

+Câu a:

A = 1/1.2 + 1/2.3 + ...+ 1/5.6 + 1

A = 1/1 - 1/2 + 1/2 - 1/3 + ...+ 1/5 - 1/6 + 1

A = 1/1 - 1/6 + 1

A = 6/6 - 1/6 + 6/6

A = 5/6 + 6/6

A = 11/6

Câu b:

B = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ...+ 1/98.99.100

B = 1/2. (2/1.2.3 + 2/2.3.4 + ...+ 2/98.99.100)

B = 1/2.(1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ...+ 1/98.99 - 1/99.100)

B = 1/2.(1/2 - 1/9900)

B = 1/2.4949/9900

B = 4949/19800