tính nhanh C = 1x3+2x4+..+17x19+18x20
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có C= 1x3+2x4+3x5+...+18x20
C= 1x(1+2)+2x(1+3)+3x(1+4)+....+18x(1+19)
C= 1x1+1x2+1x2+2x3+1x3+3x4+....+1x18+18x19
C= 1+1x2+2+2x3+3+3x4+....+18+18x19
C= (1+2+3+4+...+18) + (1x2+2x3+3x4+....+18x19)
C= 171+ (1x2+2x3+....+18x19)
Đặt A=1x2+2x3+3x4+...+18x19
3A=1x2x3+2x3x3+3x4x3+....+18x19x3
3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+.....+18x19x(20-17)
3A= 1x2x3-0+2x3x4-1x2x3+3x4x5-2x3x4+.....+18x19x20-17x18x19
3A= 18x19x20
3A= 6840
A=2280
Vậy C= 171+2280=2451
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2/2×4 + 2/4×6 + ... + 2/16×18 + 2/18×20
= 1/2 - 1/4 + 1/4 - 1/6 + ... + 1/16 - 1/18 + 1/18 - 1/20
= 1/2 - 1/20
= 10/20 - 9/20
= 9/20
2/2x4+2/4x6+...+2/16x18+2/18x20
=1/2=1/4+1/4-1/6+...+1/16-1/18+1/18-1/20
=1/2-1/20
=10/20-9/20
=1/20
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\(a,\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+....+\frac{4}{16.18}+\frac{4}{18.20}\)
\(=\frac{4}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=2.\frac{9}{20}\)
\(=\frac{9}{10}\)
\(b,\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
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