1 Tính nhanh
a)\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2015.2016}\)
b)\(B=\frac{5}{10.11}+\frac{5}{11.12}+...+\frac{5}{69.70}\)
c)\(C=\frac{12}{15.18}+\frac{12}{18.21}+...+\frac{12}{87.90}\)
Những câu hỏi liên quan
a) \(c=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
b) \(d=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)
c) \(e=\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{197.200}\)
Mik đang cần gấp
\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(B=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+...+\frac{1}{990}\)
\(C=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
A=.....
=\(7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+....+\frac{1}{69.70}\right)=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+.....+\frac{1}{69}-\frac{1}{70}\right)\)
=\(7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)
MẤY PHẦN SAU CX TÁCH MẪU RA RÙI LÀM NHƯ VẬY
TỰ LÀM NHE
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\(B=\frac{1}{3\cdot6}+\frac{1}{6\cdot9}+...+\frac{1}{30\cdot33}\)
\(B=\frac{1}{3}\cdot\left(\frac{3}{3\cdot6}+\frac{3}{6\cdot9}+...+\frac{3}{30\cdot33}\right)\)
\(B=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{30}-\frac{1}{33}\right)\)
\(B=\frac{1}{3}\cdot\left(\frac{1}{3}-\frac{1}{33}\right)\)
\(B=\frac{1}{3}\cdot\frac{10}{33}=\frac{10}{99}\)
\(C=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\)
\(C=\left(1-\frac{1}{1\cdot2}\right)+\left(1-\frac{1}{2\cdot3}\right)+...+\left(1-\frac{1}{9\cdot10}\right)\)
\(C=9-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\right)\)
\(C=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(C=9-\left(1-\frac{1}{10}\right)\)
\(C=9-\frac{9}{10}=\frac{81}{10}\)
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các bạn đều sai hết mà các bạn lại cho những câu hỏi đó đúng
Tính tổng dãy số cáh đều( tính nhanh)a, frac{7}{10.11}+ frac{7}{11.12}+.....+frac{7}{69.70}b, frac{6}{15.18}+ frac{6}{18.21}+......+frac{6}{87.60}c, frac{1}{25.27}+ frac{1}{27.29}+.......+frac{1}{73.75}d, frac{1}{1.2.3}+ frac{1}{2.3.4}+ frac{1}{3.4.5}+.....+frac{1}{18.19.20}Làm chi tiết hộ mình nha
Đọc tiếp
Tính tổng dãy số cáh đều( tính nhanh)
a, \(\frac{7}{10.11}\)+ \(\frac{7}{11.12}\)+.....+\(\frac{7}{69.70}\)
b, \(\frac{6}{15.18}\)+ \(\frac{6}{18.21}\)+......+\(\frac{6}{87.60}\)
c, \(\frac{1}{25.27}\)+ \(\frac{1}{27.29}\)+.......+\(\frac{1}{73.75}\)
d, \(\frac{1}{1.2.3}\)+ \(\frac{1}{2.3.4}\)+ \(\frac{1}{3.4.5}\)+.....+\(\frac{1}{18.19.20}\)
Làm chi tiết hộ mình nha
1) Afrac{3}{2^2}.frac{8}{3^2}.frac{15}{4^2}........frac{899}{30^2} 2) B frac{4}{3.7}+frac{4}{7.11}+frac{4}{11.15}+......+frac{4}{107.111}3) C frac{2}{15}+frac{2}{35}+frac{2}{63}+.....+frac{2}{399} 3) D frac{7}{10.11}+frac{7}{11.12}+frac{7}{12.13}+......+frac{7}{69.70} 4) E frac{6}{15.18}+frac{6}{18.21}+frac{6}{21.24}+.....+frac{6}{87.90}
Đọc tiếp
1) \(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}........\frac{899}{30^2}\) 2) B = \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+......+\frac{4}{107.111}\)
3) C = \(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+.....+\frac{2}{399}\) 3) D = \(\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+......+\frac{7}{69.70}\)
4) E =\(\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+.....+\frac{6}{87.90}\)
Tính tổng:
a) A = \(\frac{1}{2}\)+ \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\)+ .... + \(\frac{1}{23.24}\)
b) B = \(\frac{6}{15.18}\)+ \(\frac{6}{18.21}\)+ \(\frac{6}{21.24}\)+ .... + \(\frac{6}{87.90}\)
a,A=\(\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+.........+\frac{1}{23.24}\)
A=\(\frac{1}{2}+\frac{2}{1}-\frac{1}{3}+\frac{3}{1}-\frac{1}{4}+......\frac{23}{1}-\frac{1}{24}\)
A=\(\frac{1}{2}-\frac{1}{24}\)
A=\(\frac{11}{24}\)
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b)\(B=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+...+\frac{3}{87.90}\right)\)
\(=3.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(=3.\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(=3.\frac{5}{90}\)
\(=\frac{5}{30}\)
\(=\frac{1}{6}\)
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Tính:
a,\(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
b,\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
c,\(C=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{1989.1990}+...+\frac{1}{2006.2007}\)
a, \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
\(A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)
\(A=\frac{1}{11}-\frac{1}{66}\)
\(A=\frac{5}{66}\)
b, \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(B=1-\frac{1}{7}\)
\(B=\frac{6}{7}\)
_Học tốt nha_
bài 3: chứng tỏ rằng:
b) Đặt A = \(\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}
Ta có: \(A=\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}\)
\(=\frac{1}{3}(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90})\)
\(=\frac{1}{3}(\frac{1}{15}-\frac{1}{90})\)
\(=\frac{1}{3}(\frac{6}{90}-\frac{1}{90})\)
\(=\frac{1}{3}.\frac{5}{90}\)
\(=\frac{1}{54}\)
Ta có: 1= \(\frac{54}{54}\)
Suy ra A < 1 (đpcm)
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3A=3*(1/15*18+1/18*21+...+1/87*90)
3A=3/15*18+3/18*21+...+3/87*90
3A=1/15-1/18+1/18-1/21+...+1/87-1/90
3A=1/15-1/90
3A=1/18
A=1/18 chia3
A=1/54
vì 1/54<1 nên A<1
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Xem thêm câu trả lời
\(B=\frac{8}{3}.\frac{2}{5}.\frac{3}{8}.10.\frac{19}{92}\)
\(C=\frac{-5}{7}.\frac{2}{7}+\frac{-5}{7}.\frac{9}{14}+1\frac{5}{7}\)
\(D=\frac{12}{19}.\frac{7}{15}.\frac{-13}{17}.\frac{19}{12}.\frac{17}{13}\)
\(E=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
ta có;
b=8/3.2/5.3/8.10.19/92
b=16/15.3/8.10.19/92
b=2/5.10.19/92
b=4.19/92
b=19/23
c=-5/7.2/7+-5/7 . 9/14+1/5/7
c=-10/49+(-45)/98+1/5/5
c=131/98
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Tính nhanh :
a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}...+\frac{1}{98.99}+\frac{1}{99.100}\)
b)\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{41.43}\)
c)\(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)
d)\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
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