N = $\frac{1}{1.7}$ + $\frac{1}{7.13}$ + $\frac{1}{13.19}$ + . . . + $\frac{1}{1213.1219}$ 17/08/2021 Bởi Madeline N = $\frac{1}{1.7}$ + $\frac{1}{7.13}$ + $\frac{1}{13.19}$ + . . . + $\frac{1}{1213.1219}$
Tham khảo `N=\frac{1}{1.7}+\frac{1}{7.13}+….+\frac{1}{1213.1219}` `⇒6N=\frac{6}{1.7}+\frac{6}{7.13}+….+\frac{6}{1213.1219}` Áp dụng `\frac{6}{n(n+6)}=\frac{1}{n}-\frac{1}{n+6}(n \ne 0,-6)` `⇒6N=1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+….+\frac{1}{1213}-\frac{1}{1219}` `⇒6N=1-\frac{1}{1219}` `⇒6N=\frac{1218}{1219}` `⇒N=\frac{203}{1219}` `\text{©CBT}` Bình luận
Đáp án: `N=203/1219` Giải thích các bước giải: `N = 1/1.7 + 1/7.13 + … + 1/1213.1219` `= 1/6 . ( 6/1.7 + 6/7.13 + … + 6/1213.1219 )` `= 1/6 . ( 1-1/7+1/7-1/13+…+1/1213-1/1219 )` `= 1/6 . ( 1-1/1219 ) = 1/6 . 1218/1219 = 203/1219` Vậy `N=203/1219` Bình luận
Tham khảo
`N=\frac{1}{1.7}+\frac{1}{7.13}+….+\frac{1}{1213.1219}`
`⇒6N=\frac{6}{1.7}+\frac{6}{7.13}+….+\frac{6}{1213.1219}`
Áp dụng `\frac{6}{n(n+6)}=\frac{1}{n}-\frac{1}{n+6}(n \ne 0,-6)`
`⇒6N=1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+….+\frac{1}{1213}-\frac{1}{1219}`
`⇒6N=1-\frac{1}{1219}`
`⇒6N=\frac{1218}{1219}`
`⇒N=\frac{203}{1219}`
`\text{©CBT}`
Đáp án:
`N=203/1219`
Giải thích các bước giải:
`N = 1/1.7 + 1/7.13 + … + 1/1213.1219`
`= 1/6 . ( 6/1.7 + 6/7.13 + … + 6/1213.1219 )`
`= 1/6 . ( 1-1/7+1/7-1/13+…+1/1213-1/1219 )`
`= 1/6 . ( 1-1/1219 ) = 1/6 . 1218/1219 = 203/1219`
Vậy `N=203/1219`