Tính nhanh bằng cách thuận tiện
1 phần 1*6 + 1 phần 6*11 + 1 phần 11*16 + ..... + 1 phần 491*496 + 1 phần 496*501
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b, 1/1*6 + 1/6*11 + 1/11*16 ............ +1/491*496 + 1/496*501
=1/6(1-1/6+1/6-1/11+...+1/491-1/496)
=1/6(1-1/496)
=1/6.495/496
=495/2976
\(S=\frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+...+\frac{1}{496\cdot501}\)
\(S=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right)\)
\(S=\frac{1}{5}\left(1-\frac{1}{501}\right)\)
\(S=\frac{1}{5}\cdot\frac{500}{501}\)
\(S=\frac{100}{501}\)
\(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}-\frac{1}{501}\right)\)
\(=\frac{1}{5}\left(1-\frac{1}{501}\right)=\frac{1}{5}\cdot\frac{500}{501}=\frac{100}{501}\)
\(A=\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{496}-\dfrac{1}{501}\right)\)
\(=\dfrac{1}{5}\cdot\dfrac{55}{334}=\dfrac{11}{334}\)
\(B=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{21}=\dfrac{20}{21}\)
14/15 + 3/11 + 1/15 + 3/11 + 10/12
= ( 3/11 + 3/11) + (14/15 + 1/15) + 5/6
= 6/11 + 1 + 5/6
= 6/11 + 5/6 +1
= 91/66 +1
=
Đ/S:
mình trình bày hơi xấu, xin lỗi nha
bạn tự tính 91/66 + 1 nha
\(\dfrac{3}{4}.\dfrac{2}{3}-\dfrac{1}{6}.\dfrac{3}{4}-\dfrac{3}{4}.\dfrac{1}{2}\)
= \(\dfrac{3}{4}.\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)
= \(\dfrac{3}{4}.0\)
= 0
\(\dfrac{3}{4}\cdot\dfrac{2}{3}-\dfrac{1}{6}\cdot\dfrac{3}{4}-\dfrac{3}{4}\cdot\dfrac{1}{2}\)
\(=\dfrac{3}{4}\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)
\(=\dfrac{3}{4}\cdot\left(\dfrac{4}{6}-\dfrac{1}{6}-\dfrac{3}{6}\right)\)
=0
\(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{4}{6}+\frac{9}{12}+\frac{16}{20}\)
\(=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\)
\(=\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{3}{4}\right)+\left(\frac{1}{5}+\frac{4}{5}\right)\)
\(=\frac{3}{3}+\frac{4}{4}+\frac{5}{5}\)
\(=1+1+1\)
\(=3\)
\(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{4}{6}+\dfrac{9}{12}+\dfrac{16}{20}\)
\(=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{2}{3}+\dfrac{3}{4}+\dfrac{4}{5}\)
\(=\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{4}+\dfrac{3}{4}\right)+\left(\dfrac{1}{5}+\dfrac{4}{5}\right)\)
\(=\dfrac{3}{3}+\dfrac{4}{4}+\dfrac{5}{5}\)
\(=1+1+1=3\)
,r5 ơi mẹ ghi zậy ai hiểu chết liền
Nghĩa là dzậy nè:1/1x6 + 1/6x11 + 1/11x16 + ..... +1/491x496 + 1/496x501