Toán tính nhanh M= 1/15 + 1/35+1/63+1/99+…+1/2915+1/3135 06/10/2021 By Claire tính nhanh M= 1/15 + 1/35+1/63+1/99+…+1/2915+1/3135
$M=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+…+\frac{1}{2915}+\frac{1}{3135}$ $⇒2M=\frac{2}{3×5}+\frac{2}{5×7}+\frac{2}{7×9}+…+\frac{2}{53×55}+\frac{2}{55×57}$ $⇒2M=\frac{5-3}{3×5}+\frac{7-5}{5×7}+\frac{9-7}{7×9}+…+\frac{55-53}{53×55}+\frac{57-55}{55×57}$ $⇒2M=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+…+\frac{1}{53}-\frac{1}{55}+\frac{1}{55}-\frac{1}{57}$ $⇒2M=\frac{1}{3}-\frac{1}{57}$ $⇒2M=\frac{6}{19}$ $⇒M=\frac{3}{19}$. Trả lời
Đáp án: Giải thích các bước giải: `M= 1/15 + 1/35+1/63+1/99+…+1/2915+1/3135` `2M=2/3.5+2/5.7+2/7.9+2/9.11+….+2/53.55+2/55.57` `2M=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+…..+1/53-1/55+1/55-1/57` `2M=1/3-1/57=18/57=6/19` `=>M=3/19` Trả lời
$M=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+…+\frac{1}{2915}+\frac{1}{3135}$
$⇒2M=\frac{2}{3×5}+\frac{2}{5×7}+\frac{2}{7×9}+…+\frac{2}{53×55}+\frac{2}{55×57}$
$⇒2M=\frac{5-3}{3×5}+\frac{7-5}{5×7}+\frac{9-7}{7×9}+…+\frac{55-53}{53×55}+\frac{57-55}{55×57}$
$⇒2M=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+…+\frac{1}{53}-\frac{1}{55}+\frac{1}{55}-\frac{1}{57}$
$⇒2M=\frac{1}{3}-\frac{1}{57}$
$⇒2M=\frac{6}{19}$
$⇒M=\frac{3}{19}$.
Đáp án:
Giải thích các bước giải:
`M= 1/15 + 1/35+1/63+1/99+…+1/2915+1/3135`
`2M=2/3.5+2/5.7+2/7.9+2/9.11+….+2/53.55+2/55.57`
`2M=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+…..+1/53-1/55+1/55-1/57`
`2M=1/3-1/57=18/57=6/19`
`=>M=3/19`