Question

[trần ngọc diệp]

1/5x7 + 1/7x9 + 1/ 9x11 + 1/11x13 + 1/13x15

Answer 1

[Mike]

1/5*7 + 1/7*9 + 1/9*11 + ... + 1/13*15

= 1/2(2/5*7 + 2/7*9 + 2/9*11 + ... + 2/13*15)

= 1/2(1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15)

= 1/2(1/5 - 1/15)

= 1/2.2/15

= 1/15

Answer 2

[• 长αʂαƙĭ ๖ۣۜYchĭƙα ༉☆° ﾟ( Team TMS...]

Bài giải

\(\text{Đặt }A=\frac{1}{5\text{ x }7}+\frac{1}{7\text{ x }9}+\frac{1}{9\text{ x }11}+\frac{1}{11\text{ x }13}+\frac{1}{13\text{ x }15}\)

\(A=\frac{1}{2}\left(\frac{2}{5\text{ x }7}+\frac{2}{7\text{ x }9}+\frac{2}{9\text{ x }11}+\frac{2}{11\text{ x }13}+\frac{2}{13\text{ x }15}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{15}\right)\)

\(A=\frac{1}{2}\cdot\frac{2}{15}\)

\(A=\frac{1}{15}\)