A = 1/11×13 + 1/13×15 + 1/15×17 + 1/17×19 + …. + 1/97×99 05/08/2021 Bởi Josie A = 1/11×13 + 1/13×15 + 1/15×17 + 1/17×19 + …. + 1/97×99
$A=\frac{1}{11×13}+\frac{1}{13×15}+\frac{1}{15×17}+…….+\frac{1}{97×99}$ $2A=\frac{2}{11×13}+\frac{2}{13×15}+\frac{2}{15×17}+………..+\frac{2}{97×99}$ $2A=(\frac{1}{11}-\frac{1}{13})+(\frac{1}{13}-\frac{1}{15})+……+(\frac{1}{97}-\frac{1}{99}$ $2A=\frac{1}{11}-\frac{1}{99}$ $2A=\frac{8}{99}$ $A=\frac{4}{99}$ Bình luận
` A = ` ` 1/(11 xx 13) ` $+$ ` 1/(13 xx 15) ` $+$ ` 1/(15 xx 17) ` $+$ ` 1/(17 xx 19) ` $+…+$ ` 1/(97 xx 99) ` $=$ ` 1/2 xx 2 ` ` xx ` ` (1/(11 xx 13) ` $+$ ` 1/(13 xx 15) ` $+$ ` 1/(15 xx 17) ` + ` 1/(17 xx 19) ` $+…+$ ` 1/(97 xx 99)) ` $=$ ` 1/2 xx ` ` (2/(11 xx 13) ` $+$ ` 2/(13 xx 15) ` $+$ ` 2/(15 xx 17) ` $+$ ` 2/(17 xx 19) ` $+…+$ ` 2/(97 xx 99)) ` ` = 1/2 xx (1/11 – 1/13 + 1/13 – 1/15 + 1/15 – 1/17 + 1/17 – 1/19 +…+ 1/97 – 1/99) ` $=$ ` 1/2` ` xx ` ` (1/11 – 1/99 ) ` $=$ ` 1/2 ` ` xx ` ` (9/99 – 1/99 ) ` $=$ ` 1/2 ` ` xx ` ` 8/99 ` $=$ ` 4/99 ` Bình luận
$A=\frac{1}{11×13}+\frac{1}{13×15}+\frac{1}{15×17}+…….+\frac{1}{97×99}$
$2A=\frac{2}{11×13}+\frac{2}{13×15}+\frac{2}{15×17}+………..+\frac{2}{97×99}$
$2A=(\frac{1}{11}-\frac{1}{13})+(\frac{1}{13}-\frac{1}{15})+……+(\frac{1}{97}-\frac{1}{99}$
$2A=\frac{1}{11}-\frac{1}{99}$
$2A=\frac{8}{99}$
$A=\frac{4}{99}$
` A = ` ` 1/(11 xx 13) ` $+$ ` 1/(13 xx 15) ` $+$ ` 1/(15 xx 17) ` $+$ ` 1/(17 xx 19) ` $+…+$ ` 1/(97 xx 99) `
$=$ ` 1/2 xx 2 ` ` xx ` ` (1/(11 xx 13) ` $+$ ` 1/(13 xx 15) ` $+$ ` 1/(15 xx 17) ` + ` 1/(17 xx 19) ` $+…+$ ` 1/(97 xx 99)) `
$=$ ` 1/2 xx ` ` (2/(11 xx 13) ` $+$ ` 2/(13 xx 15) ` $+$ ` 2/(15 xx 17) ` $+$ ` 2/(17 xx 19) ` $+…+$ ` 2/(97 xx 99)) `
` = 1/2 xx (1/11 – 1/13 + 1/13 – 1/15 + 1/15 – 1/17 + 1/17 – 1/19 +…+ 1/97 – 1/99) `
$=$ ` 1/2` ` xx ` ` (1/11 – 1/99 ) `
$=$ ` 1/2 ` ` xx ` ` (9/99 – 1/99 ) `
$=$ ` 1/2 ` ` xx ` ` 8/99 `
$=$ ` 4/99 `