tính tổng S= \(\frac{1}{5.6}\)+\(\frac{1}{10.9}\)+\(\frac{1}{15.12}\)+....+\(\frac{1}{3350.2013}\)
cho biểu thức S= \(\frac{2}{10.12}\)+\(\frac{2}{12.14}\)+\(\frac{2}{14.16}\)+...+\(\frac{2}{98.100}\). Chứng minh S < \(\frac{1}{10}\)
Chứng minh: S < \(\frac{1}{10}\).Biết S = \(\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+.....+\frac{2}{98.100}\)
S=\(\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+.....+\frac{2}{98.100}\)
S=\(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+........+\frac{1}{98}-\frac{1}{100}\)
S=\(\frac{1}{10}-\frac{1}{100}\)
S=\(\frac{9}{100}\)<\(\frac{1}{10}\)
S=\(\frac{1}{5.6}\)+\(\frac{1}{10.9}\)+\(\frac{1}{15.12}\)+....+\(\frac{1}{3350.2013}\) Tính S
Giúp với
Tính S biết
\(S=\frac{15}{12.17}+\frac{35}{17.38}-\frac{39}{18.21}+\frac{30}{21.72}\\ S=\frac{1}{5.6}+\frac{1}{10.9}+\frac{1}{15.12}+...+\frac{1}{3350.2013}\)
Giúp mk vs m.n ơi
mk cần gấp lắm
Thanks m.n nhìu ^^
\(B=\frac{1}{5.6}+\frac{1}{10.9}+\frac{1}{15.12}+...+\frac{1}{3350.2013}\)
\(B=\frac{1}{5.3}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{670.671}\right)\)
\(B=\frac{1}{15}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{670}-\frac{1}{671}\right)\)
\(B=\frac{1}{15}.\left(1-\frac{1}{671}\right)\)
\(B=\frac{1}{15}.\frac{670}{671}=\frac{134}{2013}\)
Nguyễn Huy Thắngsoyeon_Tiểubàng giảiSilver bulletLê Nguyên HạoPhương AnVõ Đông Anh Tuấnsoyeon_Tiểubàng giảiLê Thị Linh ChiNguyễn Huy Tú
Tính tổng S = \(\frac{1}{5.6}+\frac{1}{9.10}+\frac{1}{15.12}+.....+\frac{1}{3350.2013}\)
s=\(\frac{1}{5.3.2}\) +\(\frac{1}{5.3.2.3}\) +.............+\(\frac{1}{5.3.670.671}\)
s=1/15(1/1.2+1/2.3+..................+1/670.671)
s=1/15(1-1/2+1/2-1/3+.............+1/670-1/671)
s=1/15(1-1/671)
s=1/15.670/671
s=134/2013
tính A= \(\frac{1}{5.6}+\frac{1}{10.9}+\frac{1}{15.12}+.............+\frac{1}{3350.2013}\)
GIÚP MÌNH VỚI NHÉ
Bài 2: Tính:
\(\frac{1}{10.12}+\frac{1}{12.14}+\frac{1}{14.16}+...+\frac{1}{48.50}\)
bn lấy 1/2 nhân ra ngoài ròi tính như bình thường nha!
Đặt tổng trên là A ta có
\(2A=\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{48.52}\)
\(2A=\frac{12-10}{10.12}+\frac{14-12}{12.14}+\frac{16-14}{14.16}+...+\frac{50-48}{48.50}\)
\(2A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+\frac{1}{14}-\frac{1}{16}+...+\frac{1}{48}-\frac{1}{50}=\frac{1}{10}-\frac{1}{50}=\frac{2}{25}\)
\(\Rightarrow A=\frac{2A}{2}=\frac{1}{25}\)
\(\frac{1}{10.12}+\frac{1}{12.14}+\frac{1}{14.16}+...+\frac{1}{48.50}\)
=\(\frac{1}{5.2.2.6}+\frac{1}{6.2.2.7}+\frac{1}{7.2.2.8}+...+\frac{1}{24.2.2.25}\)
=\(\frac{1}{2}.\left(\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{24.25}\right)\)
=\(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\right)\)
=\(\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{25}\right)\)
=\(\frac{1}{2}.\frac{4}{25}\)
=\(\frac{2}{25}\)
mình không biết đúng hông có gì sai cho mình xin lỗi
Tính B= \(\left(\frac{3}{429}-\frac{1}{1.3}\right)\left(\frac{3}{429}-\frac{1}{3.5}\right)....\left(\frac{3}{429}-\frac{1}{119.121}\right)\left(\frac{3}{429}-\frac{1}{121.123}\right)\)
Tính C= \(\frac{1}{5.6}+\frac{1}{10.9}+\frac{1}{15.12}+...+\frac{1}{3350.2013}\)
Tính hợp lí (nếu có thể):
\(\frac{2}{10.12}+\frac{2}{12.14}+\frac{2}{14.16}+...+\frac{2}{48.50}\)
Đặt \(A=\frac{2}{10\cdot12}+\frac{2}{12\cdot14}+\frac{2}{14\cdot16}+...+\frac{2}{48\cdot50}\)
\(A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{48}-\frac{1}{50}\)
\(A=\frac{1}{10}-\frac{1}{50}=\frac{5}{50}-\frac{1}{50}=\frac{4}{50}=\frac{2}{25}\)
Vậy \(A=\frac{2}{25}\)
= \(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{48}-\frac{1}{50}\)
= \(\frac{1}{10}-\frac{1}{50}\)= \(\frac{2}{25}\)
2/10.12+2/12.14+2/14.16+...+2/48.50
=1/10-1/12+1/12-1/14+1/14-1/16+...+1/48-1/50
=( 1/10-1/50 )+( 1/12-1/12 )+( 1/14-1/14 )+...+( 1/48-1/48 )
=( 5/50-1/50 )+0+0+...+0
=4/50
=2/25
CHÚC BẠN THÂN YÊU HỌC TỐT ^:^
A= \(\frac{1}{10.12}\)+\(\frac{1}{12.14}\)+ \(\frac{1}{14.16}\)+.........\(\frac{1}{38.40}\)
Ta có: A=\(\frac{1}{10\cdot12}+\frac{1}{12\cdot14}+\frac{1}{14\cdot16}+...+\frac{1}{38\cdot40}\)
=> \(A=\frac{1}{4}\cdot\left(\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+...+\frac{1}{19\cdot20}\right)\)
=\(\frac{1}{4}\cdot\left(\frac{6-5}{5\cdot6}+\frac{7-6}{6\cdot7}+\frac{8-7}{7\cdot8}+...+\frac{20-19}{19\cdot20}\right)\)
= \(\frac{1}{4}\cdot\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{19}-\frac{1}{20}\right)\)
= \(\frac{1}{4}\cdot\left(\frac{1}{5}-\frac{1}{20}\right)\)
= \(\frac{1}{4}\cdot\frac{3}{20}=\frac{3}{80}\)
Vậy A= 3/80
A = 1/10 - 1/12 + 1/12 - 1/14 + ....+ 1/38 - 1/40
A = 1/10 - 1/40
A = 4/40 - 1/40
A = 3/40
Chúc bạn học tốt !