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\(\frac13+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(\frac{45\times16-17}{45\times15+28}=\frac{45\times15+45-17}{45\times15+28}=\frac{45\times15+28}{45\times15+28}=1\)
Đặt A = 1.2 + 2.3 + 3.4 +.......... + 99.100
=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ..... + 99.100.(101 - 98)
=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ....... + 99.100.101 - 98.99.100
=> 3A = (1.2.3 + 2.3.4 + 3.4.5 + ....... + 99.100.101) - (1.2.3 + 2.3.4 + ......... + 98.99.100)
=> 3A = 99.100.101
=> A = 99.100.101 : 3 = 999900
2/11x13+2/13x15+2/15x17+....+2/95x97+2/97x99
=1/11-1/13+1/13-1/15+1/15-1/17+....+1/95-1/97+1/97-1/99
=1/11-1/99
=9/99-1/99
=8/99
đúng nhé bạn
2 x (2/8x10+2/10x12+....+2/38x40)
2x(1/8-1/10+1/10-1/12+...+1/38-1/40)
2x(1/8-1/40)
2x1/10
1/5
Ta có: \(\frac{1}{1\times6\times6}+\frac{1}{2\times9\times8}+\frac{1}{3\times12\times10}+\cdots+\frac{1}{98\times297\times200}\)
\(=\frac{1}{1\times3\times2}\times\left(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\cdots+\frac{1}{98\times99\times100}\right)\)
\(=\frac16\times\frac12\times\left(\frac{2}{1\times2\times3}+\frac{2}{2\times3\times4}+\cdots+\frac{2}{98\times99\times100}\right)\)
\(=\frac{1}{12}\times\left(\frac{1}{1\times2}-\frac{1}{2\times3}+\frac{1}{2\times3}-\frac{1}{3\times4}+\cdots+\frac{1}{98\times99}-\frac{1}{99\times100}\right)\)
\(=\frac{1}{12}\times\left(\frac12-\frac{1}{9900}\right)=\frac{1}{12}\times\frac{4949}{9900}=\frac{4949}{118800}\)