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làm ơn giúp mình ,bạn nào làm nhanh đúng mình chọn cho nhanh nha mọi người
C = \(\frac{6}{15.18}+\frac{6}{18.21}+...+\frac{6}{87.90}\)
C = \(2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
C = \(2.\left(\frac{1}{15}-\frac{1}{90}\right)=2.\frac{1}{18}\)
C = \(\frac{1}{9}\)
\(B=\frac{6}{1.3}+\frac{6}{3.5}+\frac{6}{5.7}+\frac{6}{7.9}+...+\frac{6}{99.101}\)
\(=3.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{9}{99.101}\right)\)
\(=3.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+....+\frac{1}{99}-\frac{1}{101}\right)\)
\(=3.\left(\frac{1}{1}-\frac{1}{101}\right)=3.\left(\frac{101}{101}-\frac{1}{101}\right)=3.\frac{100}{101}=\frac{300}{101}\)
\(C=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)
\(=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)
\(=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+....+\frac{1}{87}-\frac{1}{90}\right)\)
\(=2.\left(\frac{1}{15}-\frac{1}{90}\right)=2.\left(\frac{6}{90}-\frac{1}{90}\right)=2.\frac{5}{90}=\frac{1}{9}\)
a)Đặt \(A=\dfrac{6}{1.4}+\dfrac{6}{4.7}+\dfrac{6}{7.10}+...+\dfrac{6}{97.100}\)
\(3a=3-\dfrac{3}{4}+\dfrac{3}{4}-\dfrac{3}{7}+\dfrac{3}{7}-\dfrac{3}{10}+...+\dfrac{3}{97}-\dfrac{3}{100}\)
\(=3-\dfrac{3}{100}\)
\(=\dfrac{297}{100}\)
b)Đặt \(B=\dfrac{4}{1.3}+\dfrac{16}{3.5}+\dfrac{36}{5.7}+...+\dfrac{9604}{97.99}\)
\(=2b=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\)
\(2b=2-\dfrac{2}{3}+\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{5}-\dfrac{2}{7}+...+\dfrac{2}{97}-\dfrac{2}{99}\)
\(2b=2-\dfrac{2}{99}=\dfrac{198}{99}-\dfrac{2}{99}=\dfrac{196}{99}\)
c) Tương tự! Bạn tự làm nhé!
\(S=\frac{8.2+2.14+2.90+2.6+2.12}{2.3.4+2.8+2.79+2.11}\)
\(=\frac{2\left(8+14+90+6+12\right)}{2\left(3.4+8+79+11\right)}\)
\(=\frac{130}{110}\)
\(=\frac{13}{11}\)
(2 + 4 + 6 + ...+ 98 + 100) x (36 x 333 - 108 x 111)
= (2 + 4 + 6 + ...+ 98 + 100) x (36 x 3 x 111 - 108 x 111)
= (2 + 4 + 6 + ...+ 98 + 100) x ( 108 x 111 - 108 x 111)
= (2 + 4 + 6 + ...+ 98 + 100) x 0 = 0
a) 6 + 2 x 64 x 3 + 4 x 36
= 6 + 6 x 64 + 4 x 6 x 6
= 6 + 6 x 64 + 6 x 24
= 6 x (1 + 64 + 24)
= 6 x 89
= 534
b) 4 + 6 + 12 + ... + 2008 + 2012
= 2 x (2 + 3 + 4 + ... + 1004 + 1005)
= 2 x (2 + 1005) x 1004 : 2
= 1007 x 1004
= 1011028
mik đầu tiên nhé bạn !
a) 2.31.12+4.6.42+8.27.3
=24.31+24.42+24.27
=24.(31+42+27)
=24.100
=2400
b) 36.28+36.82+64.69+64.41
=36.(28+82)+64.(69+41)
=36.110+64.110
=110.(36+64)
=110.100
=11000