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\(P=\frac{1}{5x8}+\frac{1}{8x11}+.....+\frac{1}{602x605}\)
\(\Rightarrow3P=\frac{3}{5x8}+\frac{3}{8x11}+......+\frac{3}{602x605}\)
\(\Rightarrow3P=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-.....+\frac{1}{602}-\frac{1}{605}\)
\(\Rightarrow3P=\frac{1}{5}-\frac{1}{605}\)
\(\Rightarrow3P=\frac{24}{121}\)
\(\Rightarrow P=\frac{24}{121}:3\)
\(\Rightarrow P=\frac{8}{121}\)
\(\frac{1}{2\times5}+\frac{1}{5\times8}+\frac{1}{8\times11}+\frac{1}{11\times14}+\frac{1}{14\times17}+\frac{1}{17\times20}\)
\(=\frac{1}{3}\times\left(\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+\frac{3}{14\times17}+\frac{3}{17\times20}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\right)\)
\(=\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=\frac{1}{3}\times\frac{9}{20}\)
\(=\frac{3}{20}\)
_Chúc bạn học tốt_
Đặt \(A=\frac{1}{2x5}+\frac{1}{5x8}+..+\frac{1}{17x20}\)
\(3xA=3x\left(\frac{1}{2x5}+\frac{1}{5x8}+...+\frac{1}{17x20}\right)\)
\(3xA=\frac{3}{2x5}+\frac{3}{5x8}+....+\frac{3}{17x20}\)
\(3xA=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+..+\frac{1}{17}-\frac{1}{20}\)
\(3xA=\frac{1}{2}-\frac{1}{20}\)
\(3xA=\frac{9}{20}\)
\(\Rightarrow A=\frac{3}{20}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)
\(=\frac{1}{2}-\frac{1}{14}\)
\(=\frac{7}{14}-\frac{1}{14}\)
\(=\frac{6}{14}\)
\(=\frac{3}{7}\)
3/2x5 + 3/5x8 + 3/8x11 + 3/11x14
= 3/2 - 3/5 + 3/5 - 3/8 + 3/8 - 3/11 + 3/11 - 3/14
= 3/2 - 3/14
= 21/14 - 3/14
= 18/14
= 9/5
\(\frac{2}{5\times8}+\frac{2}{8\times11}+\frac{2}{11\times14}+...+\frac{2}{95\times98}\)
\(=\left(\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}+...+\frac{3}{95\times98}\right)\times\frac{2}{3}\)
\(=\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{95}-\frac{1}{98}\right)\times\frac{2}{3}\)
\(=\left(\frac{1}{5}-\frac{1}{98}\right)\times\frac{2}{3}\)
\(=\frac{93}{490}\times\frac{2}{3}\)
\(=\frac{93\times2}{490\times3}\)
\(=\frac{31\times1}{245\times1}\)
\(=\frac{31}{245}\)
2/5x8+2/8x11+2/11x14+...+2/95x98
=2(1/5x8+1/8x11+1/11x14+...+1/95x98) (khoang cach tu 5-8;8-11;11-14;...;95-98 la 3) suy ra =2/3(1/5-1/8+1/8-1/11+1/11-1/14+...+1/95-1/98)
=2/3(1/5-1/98)=2/3x93/5x98=31/245
= 2 x ( 1/2 x 5 + 1/ 5 x 8 + 1/ 8 x 11 + 1/ 11 x 14 + 1/ 14 x 17 )
= 2 x ( 1/2 - 1/5 + 1/5 - 1/8 + ....+1/14 - 1/17)
= 2 x (1/2 - 1/17)
= 2 x 15/34
= 15/17
ĐÚNG THÌ TÍCH CHO MÌNH NHA
CHÚC BẠN HỌC GIỎI
Đặt \(A=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\right)\)
\(A=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\)
\(A=\frac{2}{3}\cdot\frac{15}{34}=\frac{5}{17}\Rightarrow A< 1\)
1/5x8 + 1/8x11 + 1/11x14 + ... + 1/xx(x+3) = 101/1540
1/3 x (3/5x8 + 3/8x11 + 3/11x14 + ... + 3/xx(x+3) = 101/1540
1/3 x (1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + ... + 1/x - 1/x+3) = 101/1540
1/3 x (1/5 - 1/x+3) = 101/1540
1/5 - 1/x+3 = 101/1540 : 1/3
1/5 - 1/x+3 = 303/1540
1/x+3 = 1/5 - 303/1540
1/x+3 = 1/308
=> x+3=308
=> x=308-3=305
vậy x=305
1/5x8 + 1/8x11 + 1/11x14 + ... + 1/xx(x+3) = 101/1540
1/3 x (3/5x8 + 3/8x11 + 3/11x14 + ... + 3/xx(x+3) = 101/1540
1/3 x (1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + ... + 1/x - 1/x+3) = 101/1540
1/3 x (1/5 - 1/x+3) = 101/1540
1/5 - 1/x+3 = 101/1540 : 1/3
1/5 - 1/x+3 = 303/1540
1/x+3 = 1/5 - 303/1540
1/x+3 = 1/308
=> x+3=308
=> x=308-3=305
vậy x=305