\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+.....+\frac{5}{899}-\frac{5}{1023}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
11 tháng 4 2019
\(A=\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)
\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{899}{900}\)
\(=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot29}{2\cdot3\cdot4\cdot...\cdot30}\cdot\frac{3\cdot4\cdot5\cdot...\cdot31}{2\cdot3\cdot4\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)
26 tháng 3 2019
\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.........\frac{899}{30^2}\)
A= \(\frac{1.3.2.4.3.5...29.31}{2.2.3.3...30.30}\)
A=\(\frac{\left(2.3...29.30\right)\left(3.4.5...29.31\right)}{\left(2.3.4...30\right)\left(2.3.4...30\right)}\)
A=\(\frac{31}{2.30}\)
A=\(\frac{31}{60}\)
LA
11 tháng 4 2016
Ta có:
B = \(\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}.\)
= \(-5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\right)\)
= \(-5\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\)
= \(-5\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right):2\)
= \(\frac{-5}{2}\left(1-\frac{1}{51}\right)\)
= \(\frac{-5}{2}.\frac{50}{51}\) = -6375
F
28 tháng 2 2020
Bài giải
a, \(\frac{7}{12}+\frac{5}{6}+\frac{1}{4}-\frac{3}{7}-\frac{5}{12}\)
\(=\left(\frac{7}{12}-\frac{5}{12}+\frac{5}{6}+\frac{1}{4}\right)-\frac{3}{7}=\left(\frac{7}{12}-\frac{5}{12}+\frac{10}{12}+\frac{3}{12}\right)-\frac{3}{7}=\frac{5}{4}-\frac{3}{7}=\frac{23}{28}\)
b, \(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\frac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}=\frac{3^{29}\left(11-3\right)}{3^{28}\cdot4}=\frac{3\cdot8}{4}=6\)
17 tháng 8 2018
C = 1/3 + -3/4 + 3/5 + 1/57 + -1/36 + 1/15 + -2/9
C = ( 1/3 + 1/57 ) + ( -3/4 + -1/36 ) + ( 3/5 + 1/15 ) + -2/9
C = ( 19/57 + 1/57 ) + ( -27/36 + -1/36 ) + ( 9/15 + 1/15 ) + -2/9
C = 20/57 + -28/36 + 10/15 + -2/9
C = 20/57 + -7/9 + 2/3 + -2/9
C = ( 20/57 + 2/3 ) + ( -7/9 + -2/9 )
C = 58/57 + -1
C = 1/57
D = 1/2 + -1/5 + -5/7 + 1/6 + -3/35 + 1/3 + 1/41
D = ( 1/2 + 1/3 + 1/6 ) + ( -1/5 + -5/7 +-3/35 ) + 1/41
D = ( 3/6 + 2/6 + 1/6 ) + ( -7/35 + -25/35 + -3/35 ) + 1/41
D = 1 + -1 + 1/41
D = 1/41
E = -1/2 + 3/5 + -1/9 + 1/127 + -7/18 + 4/35 + 2/7
E = ( -1/2 + -1/9 + -7/18 ) + ( 3/5 + 4/35 ) + 1/127 + 2/7
E = ( -9/18 + -2/18 + -7/18 ) + ( 21/35 + 4/35 ) + 1/127 + 2/7
E = -1 + 5/7 + 1/257 + 2/7
E = -1 + ( 5/7 + 2/7 ) + 1/127
E = -1 + 1 + 1/127
E = 1/127
11 tháng 4 2016
\(B=\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}\)
\(B=\frac{-5}{1.3}+\frac{-5}{3.5}+\frac{-5}{5.7}+...+\frac{-5}{49.51}\)
\(B=\frac{-5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)
\(B=\frac{-5}{2}.\left[\left(1-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{51}\right)\right]\)
\(B=\frac{-5}{2}.\left[1-\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{49}-\frac{1}{49}\right)-\frac{1}{51}\right]\)
\(B=\frac{-5}{2}.\left(1-\frac{1}{51}\right)=\frac{-5}{2}.\frac{50}{51}=\frac{-125}{51}\)
11 tháng 4 2016
=-5/1.3+-5/3.5+-5/5.7+.............+-5/49.51
-5/2(1-1/51)
=-125/51
ai k mk mk k lai
ok
đề sai 1 tí
\(=\frac{5}{1.3}+\frac{5}{3.5}+...+\frac{5}{31.33}\)
\(=\frac{2}{5}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{33}\right)\)
\(=\frac{2}{5}\left(1-\frac{1}{33}\right)\)
\(=\frac{2}{5}\cdot\frac{32}{33}\)
\(=\frac{64}{165}\)