Tính nhanh tổng sau A=1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80 10/08/2021 Bởi Ivy Tính nhanh tổng sau A=1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80
Đặt $\frac{1}{3}$ + $\frac{1}{8}$ + $\frac{1}{15}$+ $\frac{1}{24}$+ $\frac{1}{35}$ + $\frac{1}{48}$ + $\frac{1}{63}$ + $\frac{1}{80}$ = B => 2B = $\frac{2}{3}$ + $\frac{2}{8}$ + $\frac{2}{15}$+ $\frac{2}{24}$+ $\frac{2}{35}$ + $\frac{2}{48}$ + $\frac{2}{63}$ + $\frac{2}{80}$ = $\frac{2}{1×3}$ + $\frac{2}{2×4}$ + $\frac{2}{3×5}$+ $\frac{2}{4×6}$+ $\frac{2}{5×7}$ + $\frac{2}{6×8}$ + $\frac{2}{7×9}$ + $\frac{2}{8×10}$ = 1 – $\frac{1}{3}$ + $\frac{1}{2}$ – $\frac{1}{4}$ + $\frac{1}{3}$ – $\frac{1}{5}$ + $\frac{1}{4}$ – $\frac{1}{6}$ + $\frac{1}{5}$ – $\frac{1}{7}$+ $\frac{1}{6}$ – $\frac{1}{8}$ + $\frac{1}{7}$ – $\frac{1}{9}$ + $\frac{1}{8}$ – $\frac{1}{10}$ = 1 + $\frac{1}{2}$ – $\frac{1}{9}$ – $\frac{1}{10}$ = $\frac{3}{2}$ – $\frac{1}{9}$- $\frac{1}{10}$ = $\frac{25}{18}$ -$\frac{1}{10}$ = $\frac{58}{45}$ => B = $\frac{29}{45}$ Bình luận
Đáp án:
Giải thích các bước giải:
Đặt $\frac{1}{3}$ + $\frac{1}{8}$ + $\frac{1}{15}$+ $\frac{1}{24}$+ $\frac{1}{35}$ + $\frac{1}{48}$ + $\frac{1}{63}$ + $\frac{1}{80}$ = B
=> 2B = $\frac{2}{3}$ + $\frac{2}{8}$ + $\frac{2}{15}$+ $\frac{2}{24}$+ $\frac{2}{35}$ + $\frac{2}{48}$ + $\frac{2}{63}$ + $\frac{2}{80}$
= $\frac{2}{1×3}$ + $\frac{2}{2×4}$ + $\frac{2}{3×5}$+ $\frac{2}{4×6}$+ $\frac{2}{5×7}$ + $\frac{2}{6×8}$ + $\frac{2}{7×9}$ + $\frac{2}{8×10}$
= 1 – $\frac{1}{3}$ + $\frac{1}{2}$ – $\frac{1}{4}$ + $\frac{1}{3}$ – $\frac{1}{5}$ + $\frac{1}{4}$ – $\frac{1}{6}$ + $\frac{1}{5}$ – $\frac{1}{7}$+ $\frac{1}{6}$ – $\frac{1}{8}$ + $\frac{1}{7}$ – $\frac{1}{9}$ + $\frac{1}{8}$ – $\frac{1}{10}$
= 1 + $\frac{1}{2}$ – $\frac{1}{9}$ – $\frac{1}{10}$
= $\frac{3}{2}$ – $\frac{1}{9}$- $\frac{1}{10}$
= $\frac{25}{18}$ -$\frac{1}{10}$
= $\frac{58}{45}$
=> B = $\frac{29}{45}$