Question

Giải giúp mình bài toán này nhé :

\(\frac{5}{1x7}+\frac{5}{7x13}+\frac{5}{13x19}+...+\frac{5}{91x97}\)

Nhờ các bạn giúp mình nhé ! Ai nhanh mình tick

Answer 1

Ta có:

\(\frac{5}{1\cdot7}+\frac{5}{7\cdot13}+\frac{5}{13\cdot19}+...+\frac{5}{91\cdot97}\)

= \(5\cdot\frac{1}{6}\cdot\left(\frac{6}{1\cdot7}+\frac{6}{7\cdot13}+\frac{6}{13\cdot19}+...+\frac{6}{91\cdot97}\right)\)

= \(\frac{5}{6}\cdot\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...+\frac{1}{91}-\frac{1}{97}\right)\)

= \(\frac{5}{6}\cdot\left(1-\frac{1}{97}\right)\)

= \(\frac{5}{6}\cdot\frac{96}{97}\)

= \(\frac{80}{97}\)

Answer 2

5/1.7 + 5/7.13 + 5/13.19 + ... + 5/91.97

= 5/6.(1 - 1/7 + 1/7 - 1/13 + 1/13 - 1/19 + ... + 1/91 - 1/97)

= 5/6.(1 - 1/97)

= 5/6.96/97

= 80/97

Answer 3

5/1.7+5/7.13+5/13.19+....+5/91.97

=5.(1/1.7+1/7.13+1/13.19+...+1/91.97)

=5.1/6.(6/1.7+6/7.13+6/13.19+....+6/91.97)

=5/6.(1-1/7+1/7-1/13+1/13-1/19+.....+1/91-1/97)

=5/6.(1-1/97)

=5/6.96/97

=80/97

Hok tốt

Answer 4

\(\frac{5}{1\cdot7}+\frac{5}{7\cdot13}+\cdot\cdot\cdot+\frac{5}{91\cdot97}\)

\(=\frac{5}{6}\cdot\left(\frac{6}{1\cdot7}+\frac{6}{7\cdot13}+\cdot\cdot\cdot+\frac{6}{91\cdot97}\right)\)

\(=\frac{5}{6}\cdot\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\cdot\cdot\cdot+\frac{1}{91}-\frac{1}{97}\right)\)

\(=\frac{5}{6}\cdot\left(1-\frac{1}{97}\right)\)

\(=\frac{5}{6}\cdot\frac{96}{97}\)

\(=\frac{80}{97}\)