TRONG QUYỂN NÂNG CAO PHÁT TRIỂN TOÁN 6 CÓ ĐẤY

Bạn lấy số cuối dãy trừ số đầu dãychia khoảng cách la 1 va tru 1 la tim ra so phan tu

Roi ban lay so dau day cong so cuoi daycong phan tu ban vua tinh ra chia 2

đây

Tham khảo: Câu hỏi của Nguyễn Quốc Đạt - Toán lớp 6 - Học trực tuyến OLM

A=7.(1/10.11+1/11.12+...+1/69.70)

A=7.(1/10-1/11+1/11-1/12+...+1/69-1/70)

A=7.(1/10-1/70)

A=7. 3/35

A= 3/5

chúc bạn học tốt nha

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

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

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

\(\Rightarrow A=7.\frac{6}{70}=\frac{6}{10}=\frac{3}{5}\)

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

\(\Rightarrow7A=\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}+...+\frac{1}{69\cdot70}\)

\(\Rightarrow7A=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\)

\(\Rightarrow7A=\frac{1}{10}-\frac{1}{70}\)

\(\Rightarrow7A=\frac{7}{70}-\frac{1}{70}\)

\(\Rightarrow7A=\frac{3}{35}\)

\(\Rightarrow A=\frac{3}{35}:7\)

\(\Rightarrow A=\frac{3}{245}\)

\(A=\frac{1}{7}.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{68}-\frac{1}{70}\right)\)

\(A=\frac{1}{7}.\left(\frac{1}{10}-\frac{1}{70}\right)=\frac{1}{7}.\frac{3}{35}=\frac{3}{245}\)

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

A=\(\frac{7}{10}\)-\(\frac{7}{11}\)+\(\frac{7}{11}\)-\(\frac{7}{12}\)+\(\frac{7}{12}\)-\(\frac{7}{13}\)+...+\(\frac{7}{69}\)-\(\frac{7}{70}\)

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

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

Ạ=\(\frac{6}{10}=\frac{3}{5}\).

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

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

=\(7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{21}{35}\)

Lời giải:

$3S=10.11(12-9)+11.12(13-10)+12.13(14-11)+...+98.99(100-97)+99.100(101-98)$

$=(10.11.12+11.12.13+12.13.14+...+98.99.100+99.100.101)-(9.10.11+10.11.12+...+97.98.99+98.99.100)$

$=99.100.101-9.10.11$

$\Rightarrow S=\frac{99.100.101-9.10.11}{3}=33.100.101-3.10.11$

=1/10 - 1/11+......+1/99-1/100

=1/10-1/100

=9/100