2/3+14/15+34/35+62/63+98/99+142/143+194/195 12/08/2021 Bởi Alaia 2/3+14/15+34/35+62/63+98/99+142/143+194/195
Đáp án: $\frac{98}{15}$ Giải thích các bước giải: A = $\frac{2}{3}$ + $\frac{14}{15}$ + $\frac{34}{35}$ + $\frac{62}{63}$ + $\frac{98}{99}$ + $\frac{142}{143}$ + $\frac{194}{195}$ = (1 – $\frac{1}{3}$) + (1 – $\frac{1}{15}$) + (1 – $\frac{1}{35}$) + (1 – $\frac{1}{63}$) + (1 – $\frac{1}{99}$) + (1 – $\frac{1}{143}$) + (1 – $\frac{1}{195}$) = (1 + 1 + 1 + 1 + 1 + 1 + 1) – ($\frac{1}{3}$ + $\frac{1}{15}$ + $\frac{1}{35}$ + $\frac{1}{63}$ + $\frac{1}{99}$ + $\frac{1}{143}$ + $\frac{1}{195}$) = 7 – ($\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + $\frac{1}{7.9}$ + $\frac{1}{9.11}$ + $\frac{1}{11.13}$ + $\frac{1}{13.15}$) Đặt S = $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + $\frac{1}{7.9}$ + $\frac{1}{9.11}$ + $\frac{1}{11.13}$ + $\frac{1}{13.15}$ ⇒ A = 7 – S Ta có: 2S = 2.($\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + $\frac{1}{7.9}$ + $\frac{1}{9.11}$ + $\frac{1}{11.13}$ + $\frac{1}{13.15}$) = $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ + $\frac{2}{7.9}$ + $\frac{2}{9.11}$ + $\frac{2}{11.13}$ + $\frac{2}{13.15}$ = 1 – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{5}$ + $\frac{1}{5}$ – $\frac{1}{7}$ + $\frac{1}{7}$ – $\frac{1}{9}$ + $\frac{1}{9}$ – $\frac{1}{11}$ + $\frac{1}{11}$ – $\frac{1}{13}$ + $\frac{1}{13}$ – $\frac{1}{15}$ = 1 – $\frac{1}{15}$ = $\frac{14}{15}$ ⇒ S = $\frac{14}{15}$ : 2 = $\frac{7}{15}$ ⇒ A = 7 – S = 7 – $\frac{7}{15}$ = $\frac{98}{15}$ Vậy A = $\frac{2}{3}$ + $\frac{14}{15}$ + $\frac{34}{35}$ + $\frac{62}{63}$ + $\frac{98}{99}$ + $\frac{142}{143}$ + $\frac{194}{195}$ = $\frac{98}{15}$ Chúc bn học tốt! Bình luận
Đáp án:
$\frac{98}{15}$
Giải thích các bước giải:
A = $\frac{2}{3}$ + $\frac{14}{15}$ + $\frac{34}{35}$ + $\frac{62}{63}$ + $\frac{98}{99}$ + $\frac{142}{143}$ + $\frac{194}{195}$
= (1 – $\frac{1}{3}$) + (1 – $\frac{1}{15}$) + (1 – $\frac{1}{35}$) + (1 – $\frac{1}{63}$) + (1 – $\frac{1}{99}$) + (1 – $\frac{1}{143}$) + (1 – $\frac{1}{195}$)
= (1 + 1 + 1 + 1 + 1 + 1 + 1) – ($\frac{1}{3}$ + $\frac{1}{15}$ + $\frac{1}{35}$ + $\frac{1}{63}$ + $\frac{1}{99}$ + $\frac{1}{143}$ + $\frac{1}{195}$)
= 7 – ($\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + $\frac{1}{7.9}$ + $\frac{1}{9.11}$ + $\frac{1}{11.13}$ + $\frac{1}{13.15}$)
Đặt S = $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + $\frac{1}{7.9}$ + $\frac{1}{9.11}$ + $\frac{1}{11.13}$ + $\frac{1}{13.15}$
⇒ A = 7 – S
Ta có: 2S = 2.($\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + $\frac{1}{7.9}$ + $\frac{1}{9.11}$ + $\frac{1}{11.13}$ + $\frac{1}{13.15}$)
= $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ + $\frac{2}{7.9}$ + $\frac{2}{9.11}$ + $\frac{2}{11.13}$ + $\frac{2}{13.15}$
= 1 – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{5}$ + $\frac{1}{5}$ – $\frac{1}{7}$ + $\frac{1}{7}$ – $\frac{1}{9}$ + $\frac{1}{9}$ – $\frac{1}{11}$ + $\frac{1}{11}$ – $\frac{1}{13}$ + $\frac{1}{13}$ – $\frac{1}{15}$
= 1 – $\frac{1}{15}$ = $\frac{14}{15}$
⇒ S = $\frac{14}{15}$ : 2 = $\frac{7}{15}$
⇒ A = 7 – S = 7 – $\frac{7}{15}$ = $\frac{98}{15}$
Vậy A = $\frac{2}{3}$ + $\frac{14}{15}$ + $\frac{34}{35}$ + $\frac{62}{63}$ + $\frac{98}{99}$ + $\frac{142}{143}$ + $\frac{194}{195}$ = $\frac{98}{15}$
Chúc bn học tốt!