Question

 

 

Giup mình giải bài toán nâng cao này với: 

7/10x11 + 7/11x12 + 7/12x13 +...+ 7/69x70 =?

Answer 1

7/10x11+7/11x12+7/12x13+.................+7/69x70
=1x7/10x11+1x7/11x12+...........+1x7/69x70
=7(1/10x11+1/11x12+1/12x13+....+1/69x70)
=7(1/10‐1/11+1/11‐1/12+1/12‐1/13+.......+1/69‐1/70)
=7(1/10‐1/70)
=7(7/70‐1/70)
=7x6/70

=3/5

NHỚ TK MK NHA

Answer 2

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

\(7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{7-1}{70}=\frac{6}{10}=\frac{3}{5}\)

Answer 3

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

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

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

\(A=7.\frac{3}{35}\)

\(A=\frac{3}{5}\)

Answer 4

Gọi tổng cần tìm là S.

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

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

S : 7 = \(\frac{1}{10.11}\) + \(\frac{1}{11.12}\) + \(\frac{1}{12.13}\) + ...+  \(\frac{1}{69.70}\)

S : 7 = \(\frac{1}{10}\) -  \(\frac{1}{11}\) + \(\frac{1}{11}\) - \(\frac{1}{12}\) + \(\frac{1}{12}\) - \(\frac{1}{13}\) + ... + \(\frac{1}{69}\) - \(\frac{1}{70}\)

S : 7 = \(\frac{1}{10}\) - \(\frac{1}{70}\)

S : 7 =       \(\frac{3}{35}\)

S      = \(\frac{3}{35}\) . 7 = \(\frac{3}{5}\)

Answer 5

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

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

\(=7\cdot\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{68}-\frac{1}{69}+\frac{1}{69}-\frac{1}{70}\right)\)

\(=7\cdot\left(\frac{1}{10}-\frac{1}{70}\right)=7\cdot\frac{7-1}{70}=7\cdot\frac{6}{70}=\frac{3}{5}\)

Answer 6

B = \(\frac{7}{10x11}+\frac{7}{11x12}+\frac{7}{12x13}+........+\frac{7}{69x70}\)

=> B : 7 = \(\frac{1}{10x11}+\frac{1}{11x12}+\frac{1}{12x13}+.......+\frac{1}{69x70}\)

B : 7 = \(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+........+\frac{1}{69}-\frac{1}{70}\)

=> B : 7 = \(\frac{1}{10}-\frac{1}{70}\)= \(\frac{7}{70}-\frac{1}{70}=\frac{6}{70}\)

=> B = \(\frac{6}{70}x7\)= \(\frac{3}{5}\)

Answer 7

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

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

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

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

\(=7.\frac{3}{35}\)

\(=\frac{3}{5}\)