Tính nhanh:
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{49.50}\)
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DT
23 tháng 10 2023 lúc 19:40
Tính nhanh
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\)
ta nhận thấy
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/30=1/5-1/6
1/42=1/6-1/7
ta có:
1/2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
bn tự hiểu nha
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Tính nhanh: \(\dfrac{1}{2}\)+ \(\dfrac{1}{6}\)+ \(\dfrac{1}{12}\)+ \(\dfrac{1}{20}\) + ... + \(\dfrac{1}{90}\)
sau đây là phần chữa của mình:
\(=\dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{10}\)
= \(\dfrac{3}{10}\)
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= \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
= \(\dfrac{1}{2}-\dfrac{1}{10}\)
= \(\dfrac{2}{5}\)
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chỗ đầu mình quên cộng thêm 1/2 rồi bạn nhớ bổ sung nha thì sẽ ra kết quả đúng nhé
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SC
16 tháng 10 2021 lúc 15:24
VÒNG 2Bài 1: Mèo con nhanh nhẹndfrac{1}{2} + dfrac{1}{12}2 + dfrac{1}{6}dfrac{1}{20}1 - dfrac{1}{9} dfrac{1}{15} + dfrac{2}{15}dfrac{1}{2} + dfrac{2}{3}dfrac{7}{12}dfrac{4}{12} dfrac{9}{14}+ dfrac{1}{14}1 + dfrac{1}{6}dfrac{1}{4} - dfrac{1}{5}dfrac{1}{3} - dfrac{2}{9} dfrac{3}{2} + dfrac{2}{3}dfrac{1}{5}1 - dfrac{8}{9} dfrac{5}{7}1 - dfrac{2}{3}dfrac{1}{3} + dfrac{5}{9}
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VÒNG 2
Bài 1: Mèo con nhanh nhẹn
| \(\dfrac{1}{2}\) + \(\dfrac{1}{12}\) | 2 + \(\dfrac{1}{6}\) | \(\dfrac{1}{20}\) | 1 - \(\dfrac{1}{9}\) | |
| \(\dfrac{1}{15}\) + \(\dfrac{2}{15}\) | \(\dfrac{1}{2}\) + \(\dfrac{2}{3}\) | \(\dfrac{7}{12}\) | \(\dfrac{4}{12}\) | |
| \(\dfrac{9}{14}\)+ \(\dfrac{1}{14}\) | 1 + \(\dfrac{1}{6}\) | \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) | \(\dfrac{1}{3}\) - \(\dfrac{2}{9}\) | |
| \(\dfrac{3}{2}\) + \(\dfrac{2}{3}\) | \(\dfrac{1}{5}\) | 1 - \(\dfrac{8}{9}\) | ||
| \(\dfrac{5}{7}\) | 1 - \(\dfrac{2}{3}\) | \(\dfrac{1}{3}\) + \(\dfrac{5}{9}\) |
ML
SGK Kết nối tri thức với cuộc sống - Trang 81
24 tháng 8 2023 lúc 0:54
Tính (theo mẫu).Mẫu: dfrac{1}{2}-dfrac{5}{12}dfrac{6}{12}-dfrac{5}{12}dfrac{6-5}{12}dfrac{1}{12}a) dfrac{3}{4}-dfrac{1}{8} b) dfrac{2}{6}-dfrac{5}{18} c) dfrac{2}{5}-dfrac{3}{20}
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Tính (theo mẫu).
| Mẫu: \(\dfrac{1}{2}-\dfrac{5}{12}=\dfrac{6}{12}-\dfrac{5}{12}=\dfrac{6-5}{12}=\dfrac{1}{12}\) |
a) \(\dfrac{3}{4}-\dfrac{1}{8}\) b) \(\dfrac{2}{6}-\dfrac{5}{18}\) c) \(\dfrac{2}{5}-\dfrac{3}{20}\)
a) \(\dfrac{3}{4}-\dfrac{1}{8}=\dfrac{6}{8}-\dfrac{1}{8}=\dfrac{6-1}{8}=\dfrac{5}{8}\)
b) \(\dfrac{2}{6}-\dfrac{5}{18}=\dfrac{6}{18}-\dfrac{5}{18}=\dfrac{6-5}{18}=\dfrac{1}{18}\)
c) \(\dfrac{2}{5}-\dfrac{3}{20}=\dfrac{8}{20}-\dfrac{3}{20}=\dfrac{8-3}{20}=\dfrac{5}{20}=\dfrac{1}{4}\)
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a) Tính :
\(1-\dfrac{1}{2};\dfrac{1}{2}-\dfrac{1}{3};\dfrac{1}{3}-\dfrac{1}{4};\dfrac{1}{4}-\dfrac{1}{5};\dfrac{1}{5}-\dfrac{1}{6}\)
b) Sử dụng kết quả của câu a) để tính nhanh tổng sau :
\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
a) \(1-\dfrac{1}{2}=\dfrac{1}{2}\)
\(\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{3-2}{6}=\dfrac{1}{6}\)
\(\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{4-3}{12}=\dfrac{1}{12}\)
\(\dfrac{1}{4}-\dfrac{1}{5}=\dfrac{5-4}{20}=\dfrac{1}{20}\)
\(\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{6-5}{30}=\dfrac{1}{30}\)
b) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
\(=\left(1-\dfrac{1}{2}\right)+\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{1}{3}-\dfrac{1}{4}\right)+\left(\dfrac{1}{4}-\dfrac{1}{5}\right)+\left(\dfrac{1}{5}+\dfrac{1}{6}\right)\)
\(=1+\left(-\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(-\dfrac{1}{3}+\dfrac{1}{3}\right)+\left(-\dfrac{1}{4}+\dfrac{1}{4}\right)+\left(-\dfrac{1}{5}+\dfrac{1}{5}\right)+-\dfrac{1}{6}\)\(=1+-\dfrac{1}{6}\)
\(=\dfrac{5}{6}\)
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\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\).Tính
ok luôn.hay thì like nha
ta có
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=1/1*2+1/2*3+1/3*4+...+1/8*9
=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9
=1-1/9
=8/9
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TM
8 tháng 12 2021 lúc 11:27
Tính: \(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{7}-\dfrac{1}{8}\)
\(A=1-\dfrac{1}{8}=\dfrac{7}{8}\)
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\(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
\(A=\dfrac{367}{420}\approx0,87\)
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A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72
= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9
= 1/1 − 1/2 + 1/2 − 1/3 + 1/3 − 1/4 + 1/4 − 1/5 + 1/5 − 1/6 + 1/6 − 1/7 + 1/7 − 1/8 + 1/8 − 1/9
= 1 − 1/9
= 8/9
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Tính nhanh:
a, \(\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)
b, \(\left(-\dfrac{1}{4}+\dfrac{7}{35}-\dfrac{5}{3}\right)-\left(-\dfrac{15}{12}+\dfrac{6}{11}-\dfrac{48}{49}\right)\)
a: Ta có: \(\dfrac{8}{9}-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{72}\right)\)
\(=\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{3}-...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
=0
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Tính nhanh:
\(\dfrac{1}{6}\) + \(\dfrac{7}{12}\) - \(\dfrac{9}{20}\) + \(\dfrac{11}{30}\) - \(\dfrac{13}{42}\)
\(\dfrac{1}{6}+\dfrac{7}{12}-\dfrac{9}{20}+\dfrac{11}{30}-\dfrac{13}{42}\)
\(=\dfrac{1}{2.3}+\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}-\left(\dfrac{1}{4}+\dfrac{1}{5}\right)+\dfrac{1}{5}+\dfrac{1}{6}-\left(\dfrac{1}{6}+\dfrac{1}{7}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{7}=\dfrac{5}{14}\)
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