a) 123,45 x 678 - 246,9 x 338 - 246

= 83699,1 - 83452,2 - 246

= 246,9 - 246

= 0,9

b, \(\frac{1}{6}+\frac{1}{11}+\frac{1}{70}+\frac{1}{126}+\frac{1}{198}+\frac{1}{286}\)

Bạn tính ra máy tính bỏ túi

a) 0,9

b) 1237/4290

lam rõ nha các bn

làm nhanh mk sẽ k

Đặt A=\(\frac{1}{15}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

Ta có:

A=\(\frac{1}{15}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

=>A=\(\frac{1}{3.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)

=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)

=\(\frac{1}{3}-\frac{1}{20}\)

=\(\frac{17}{60}\)

Câu b bạn đặt B bằng từng đó rồi nhân 2B lên và phân tách rồi giãn ước 6=1.6,60=6.10,140=10.140,v.v

Tính được kết quả thì chia 2

Câu hỏi của Thịnh - Toán lớp 6 - Học toán với OnlineMath

Bạn tham khảo câu hỏi ở link này.

Đề lỗi. mk sửa 15->10

\(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

\(=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)

\(=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)

\(=\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\right)\)

\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)

\(=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=\frac{1}{3}.\frac{9}{20}\)

\(=\frac{9}{60}\)

Đặt \(S=\frac{1}{6}+\frac{1}{30}+\frac{1}{70}+\frac{1}{126}+\frac{1}{198}+\frac{1}{286}\)

\(\Leftrightarrow2S=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\)

\(\Leftrightarrow2S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)

\(\Leftrightarrow4S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\)

\(\Leftrightarrow4S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\)

\(\Leftrightarrow4S=1-\frac{1}{13}\)

\(\Leftrightarrow4S=\frac{12}{13}\)

\(\Leftrightarrow S=\frac{12}{13}\div4\)

\(\Leftrightarrow S=\frac{3}{13}\)

hai câu khác nhau hả bạn

123,45.678-246,9.338-246=83699,1-83452,-246

=0,9

\(\dfrac{1}{6}+\dfrac{1}{11}+\dfrac{1}{70}+\dfrac{1}{26}\)

=\(\dfrac{5005+2730+429+1155}{30030}\)

=\(\dfrac{9319}{30030}\)

hai phần khác nhau nhé các bạn

\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(A=7\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{69.70}\right)\)

\(A=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+....+\frac{1}{69}-\frac{1}{70}\right)\)

\(A=7\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(A=7\cdot\frac{3}{35}=\frac{21}{35}\)

\(A=\frac{7}{10\cdot11}+\frac{7}{11\cdot12}+\frac{7}{12\cdot13}+...+\frac{7}{69\cdot70}\)

\(A=7\left(\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}+...+\frac{1}{69\cdot70}\right)\)

\(A=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(A=7\left(\frac{1}{10}-\frac{1}{70}\right)=7\cdot\frac{3}{35}=\frac{3}{5}\)

\(B=\frac{1}{25\cdot27}+\frac{1}{27\cdot29}+\frac{1}{29\cdot31}+...+\frac{1}{73\cdot75}\)

\(B=\frac{1}{2}\left(\frac{2}{25\cdot27}+\frac{2}{27\cdot29}+\frac{2}{29\cdot31}+...+\frac{2}{73\cdot75}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)

\(B=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)

\(C=\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{2008\cdot2010}\)

\(C=\frac{4}{2}\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{2008\cdot2010}\right)\)

\(C=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(C=2\left(\frac{1}{2}-\frac{1}{2010}\right)=2\cdot\frac{502}{1005}=\frac{1004}{1005}\)

\(B=\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(2B=\frac{2}{25.27}+\frac{2}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

\(2B=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\)

\(2B=\frac{1}{25}-\frac{1}{75}=\frac{2}{75}\)

=>2A=4/2*6+4/6*10+4/10*14+...+4/42*46

=>2A=1/2-1/6+1/6-1/10+...+1/42-1/46=1/2-1/46=22/46

=>A=11/46

\(A=\dfrac{1}{6}+\dfrac{1}{30}+\dfrac{1}{70}+\dfrac{1}{126}+...+\dfrac{1}{966}\)

\(\Rightarrow\dfrac{4}{2}A=\dfrac{4}{2}\cdot\left(\dfrac{1}{6}+\dfrac{1}{30}+\dfrac{1}{70}+...+\dfrac{1}{966}\right)\)

\(\Rightarrow2A=\dfrac{4}{2\times6}+\dfrac{4}{6\times10}+\dfrac{4}{10\times14}+\dfrac{4}{14\times18}+...+\dfrac{4}{42\times46}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{18}+...+\dfrac{1}{42}-\dfrac{1}{46}\)

\(\Rightarrow2A=\dfrac{1}{2}-\dfrac{1}{46}\)

\(\Rightarrow2A=\dfrac{11}{23}\)

\(\Rightarrow A=\dfrac{11}{23}:2\)

\(\Rightarrow A=\dfrac{11}{46}\)