Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(S=\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+....+\frac{90}{4}\)
\(=\frac{1+2+3+...+90}{4}\)
\(=\frac{\frac{90\left(90+1\right)}{2}}{4}\)
\(=\frac{4095}{4}\)
Bài này được cái rối mắt thôi :')))
\(\frac{1}{1+\frac{2}{3+\frac{4}{5+\frac{6}{7}}}}+\frac{1}{1+\frac{1}{2+\frac{3}{4+\frac{4}{5}}}}=\frac{1}{1+\frac{2}{3+\frac{4}{\frac{41}{7}}}}+\frac{1}{1+\frac{1}{2+\frac{3}{\frac{24}{5}}}}\)
\(=\frac{1}{1+\frac{2}{3+\frac{28}{41}}}+\frac{1}{1+\frac{1}{2+\frac{5}{8}}}=\frac{1}{1+\frac{2}{\frac{151}{41}}}+\frac{1}{1+\frac{1}{\frac{21}{8}}}\)
\(=\frac{1}{1+\frac{8}{151}}+\frac{1}{1+\frac{8}{21}}=\frac{1}{\frac{159}{151}}+\frac{1}{\frac{29}{21}}=\frac{151}{159}+\frac{21}{29}\)
a)
\(\begin{array}{l}\left( {\frac{{ - 2}}{{ - 5}}:\frac{3}{{ - 4}}} \right).\frac{4}{5} = \left( {\frac{2}{5}.\frac{{ - 4}}{3}} \right).\frac{4}{5}\\ = \frac{{ - 8}}{{15}}.\frac{4}{5} = \frac{{ - 32}}{{75}}\end{array}\)
b)
\(\begin{array}{l}\frac{{ - 3}}{{ - 4}}:\left( {\frac{7}{{ - 5}}.\frac{{ - 3}}{2}} \right) = \frac{3}{4}:\frac{{ - 21}}{{ - 10}}\\ = \frac{3}{4}.\frac{{10}}{{21}} = \frac{{30}}{{84}} = \frac{5}{14}\end{array}\)
c)
\(\begin{array}{l}\frac{{ - 1}}{9}.\frac{{ - 3}}{5} + \frac{5}{{ - 6}}.\frac{{ - 3}}{5} + \frac{5}{2}.\frac{{ - 3}}{5}.\\ = \frac{{ - 3}}{5}.\left( {\frac{{ - 1}}{9} + \frac{5}{{ - 6}} + \frac{5}{2}} \right)\\ = \frac{{ - 3}}{5}.\left( {\frac{{ - 2}}{{18}} + \frac{{ - 15}}{{18}} + \frac{{45}}{{18}}} \right)\\ = \frac{{ - 3}}{5}.\frac{{28}}{{18}}\\ = \frac{{ - 3}}{5}.\frac{{14}}{9}\\ = \frac{{ - 14}}{{15}}\end{array}\)
Mình lộn
S = \(\frac{\left(1+90\right)\times90\div2}{4}\)
S = \(\frac{4095}{4}\)
Tổng dãy đó là
\(\left(\frac{90}{4}+\frac{1}{4}\right)\times\left[\left(\frac{90}{4}-\frac{1}{4}\right)\div\frac{1}{4}+1\right]\div2=\)\(=\frac{4095}{4}\)
Đáp số : \(\frac{4095}{4}\)