Bài 9 : tính :
A = \(\dfrac{1}{2.9}\) +\(\dfrac{1}{9.7}\) +\(\dfrac{1}{7.19}\) +....+\(\dfrac{1}{252.509}\)
B = \(\dfrac{1}{10.9}\) + \(\dfrac{1}{18.13}\) + \(\dfrac{1}{26.17}\) + ... + \(\dfrac{1}{802.405}\)
Tính
a) A = \(\dfrac{1}{2.9}+\dfrac{1}{9.7}+\dfrac{1}{7.19}+...+\dfrac{1}{252.509}\)
b) B =\(\dfrac{1}{10.9}+\dfrac{1}{18.13}+\dfrac{1}{26.17}+...+\dfrac{1}{802.405}\)
c) C = \(\dfrac{2}{4.7}-\dfrac{3}{5.9}+\dfrac{2}{7.10}-\dfrac{3}{9.13}+...+\dfrac{2}{301.304}-\dfrac{3}{401.405}\)
giúp mk với
b)\(\dfrac{1}{7}B=\dfrac{1}{10.18}+\dfrac{1}{18.26}+\dfrac{1}{26.34}+...+\dfrac{1}{802.810}\)
\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{8}{10.18}+\dfrac{8}{18.26}+\dfrac{8}{26.34}+...+\dfrac{8}{802.810}\right)\)
\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{1}{10}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{34}+...+\dfrac{1}{802}-\dfrac{1}{810}\right)\)
\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{1}{10}-\dfrac{1}{810}\right)\)
\(\dfrac{1}{7}B=\dfrac{1}{8}.\dfrac{8}{81}\)
\(\dfrac{1}{7}B=\dfrac{1.8}{8.81}\)
\(\dfrac{1}{7}B=\dfrac{1}{81}\)
\(B=\dfrac{1}{81}:\dfrac{1}{7}\)
\(B=\dfrac{7}{81}\)
Chung minh A<\(\dfrac{1}{10}\) biet :
A=\(\dfrac{1}{2.9}+\dfrac{1}{9.7}+\dfrac{1}{7.19}+......+\dfrac{1}{252.509}\)
\(\dfrac{5}{2}A=\dfrac{5}{4.9}+\dfrac{5}{9.14}+\dfrac{5}{14.19}+...+\dfrac{5}{504.509}\)
\(\dfrac{5}{2}A=\dfrac{9-4}{4.9}+\dfrac{14-9}{9.14}+\dfrac{19-14}{14.19}+...+\dfrac{509-504}{504.509}\)
\(\dfrac{5}{2}A=\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{504}-\dfrac{1}{509}\)
\(\dfrac{5}{2}A=\dfrac{1}{4}-\dfrac{1}{509}\)
\(A=\left(\dfrac{1}{4}-\dfrac{1}{509}\right).\dfrac{2}{5}\)
\(A=\dfrac{1}{10}-\dfrac{2}{2545}< \dfrac{1}{10}\)
\(\Rightarrow A< \dfrac{1}{10}\)(đpcm)
Chúc bạn học tốt!
Ta có:
A=\(\dfrac{1}{2.9}+\dfrac{1}{9.7}+\dfrac{1}{7.19}+...+\dfrac{1}{252.509}\)
A=2.(\(\dfrac{1}{4.9}+\dfrac{1}{9.14}+\dfrac{1}{14.19}+...+\dfrac{1}{504.509}\))
A=\(\dfrac{2}{5}\).(\(\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{19}+...+\dfrac{1}{504}-\dfrac{1}{509}\))
A=\(\dfrac{2}{5}\).(\(\dfrac{1}{4}-\dfrac{1}{509}\))
A=\(\dfrac{2}{5}\).(\(\dfrac{509}{2036}-\dfrac{4}{2036}\))
A=\(\dfrac{2}{5}\).\(\dfrac{505}{2036}\)
A=\(\dfrac{101}{1018}\)
Sử dụng điều kiện \(\dfrac{n}{a\left(a+n\right)}=\dfrac{1}{a}-\dfrac{1}{a+n}\) để tính:
a. \(A=\dfrac{1}{2.9}+\dfrac{1}{9.7}+\dfrac{1}{7.19}+...+\dfrac{1}{252.509}\)
b.\(B=\dfrac{2}{4.7}-\dfrac{3}{5.9}+\dfrac{2}{7.10}-\dfrac{3}{9.13}+...+\dfrac{2}{301.304}-\dfrac{3}{401.405}\)
A=1/2.9+1/9.7+1/7.19+...+1/252.509
=?
??????
Tính
a) A= 1/2.9 + 1/9.7 + 1/7.19 +....+ 1/252.509
b) B= 1/10.9 + 1/18.13 + 1/26.17+.... + 1/802.405
Nhanh nhaaa iuuu
a)Ta có:
A= 1/2.9 + 1/9.7 +...+1/252.509
= 2/5.(5/4.9 + 5/9.14 + 5/14.19 +...+ 1/504.509)
= 2/5.(1/4 - 1/9 + 1/9 - 1/14 + 1/14 - 1/19 +...+ 1/504 - 1/509)
= 2/5.(1/4 - 1/509)
= 101/1018
Vậy A = 101/1018
b)Ta có:
B= 1/10.9 +1/18.13 + 1/26.17 +...+ 1/802.405)
= 1/4.(8/10.18 + 8/18.26 + 8/26.34 +...+ 8/802.810)
= 1/4.(1/10 - 1/18 + 1/18 - 1/26 + 1/26 - 1/34 +...+ 1/802 - 1/810)
= 1/4.(1/10 - 1/810)
= 2/81
Vậy B= 2/81
Tk mình nha!!!
bài 1 : tính
\(B=\dfrac{1}{10.9}+\dfrac{1}{18.13}+\dfrac{1}{26.27}+...+\dfrac{1}{802.405}\)
\(D=\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{10}}+...-\dfrac{1}{2^{58}}\)
mn giúp mk gấp nhé !!
Tính :
a)A=1/2.9 + 1/9.7 + 1/7.19 + ...+1/252.509
b)B=1/10.9 + 1/18.13 + 1/26.17 + ... + 1/802.405
c)C=2/4.7 - 3/5.9 +2/7.10 - 3/9.13+...+2/301.304 - 3/401.405
\(A=\frac{1}{2.9}+\frac{1}{9.7}+...+\frac{1}{252.509}\)
\(A=\frac{2}{4.9}+\frac{2}{9.14}+...+\frac{2}{504.509}\)
\(A=\frac{2}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{504.509}\right)\)
\(A=\frac{2}{5}.\left(\frac{9-4}{4.9}+\frac{14.9}{9.14}+...+\frac{509-504}{504.509}\right)\)
\(A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{504}-\frac{1}{509}\right)\)
\(A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{509}\right)\)
\(A=\frac{2}{5}.\frac{505}{2036}\)
\(A=\frac{101}{1018}\)
\(B=\frac{1}{10.9}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405}\)
\(\frac{1}{2}B=\frac{1}{10.9.2}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405.2}\)
\(\frac{1}{2}B=\frac{1}{10.18}+\frac{1}{18.26}+\frac{1}{26.34}+...+\frac{1}{802.810}\)
\(4B=\frac{8}{10.18}+\frac{8}{18.26}+\frac{8}{26.34}+...+\frac{8}{802.810}\)
\(4B=\frac{18-10}{10.18}+\frac{26-18}{28.26}+\frac{34-26}{26.34}+...+\frac{810-802}{802.810}\)
\(4B=\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+\frac{1}{26}-\frac{1}{34}+...+\frac{1}{802}-\frac{1}{810}\)
\(4B=\frac{1}{10}-\frac{1}{810}\)
\(4B=\frac{8}{81}\)
\(B=\frac{2}{81}\)
\(C=\frac{2}{4.7}-\frac{3}{5.9}+\frac{2}{7.10}-\frac{3}{9.13}+...+\frac{2}{301.304}-\frac{3}{401.405}\)
\(C=\left(\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{301.304}\right)-\left(\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{401.405}\right)\)
\(C=\frac{2}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)-\frac{3}{4}.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{401}-\frac{1}{405}\right)\)
\(C=\frac{2}{3}.\left(\frac{1}{4}-\frac{1}{304}\right)-\frac{3}{4}.\left(\frac{1}{5}-\frac{1}{405}\right)\)
\(C=\frac{2}{3}.\frac{75}{304}-\frac{3}{4}.\frac{16}{81}\)
\(C=\frac{25}{152}-\frac{4}{27}\)
\(C=\frac{67}{4104}\)
tính nhanh :
A = \(\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+......+\frac{1}{252.509}\)
B = \(\frac{1}{10.9}+\frac{1}{18.13}+\frac{1}{26.17}+......+\frac{1}{802.405}\)
Bài 1. Tính
A= \(\left(8\dfrac{2}{7}-4\dfrac{2}{7}\right)-3\dfrac{4}{9}\)
B= \(\left(10\dfrac{2}{9}-6\dfrac{2}{9}\right)+2\dfrac{3}{5}\)
Bài 2. Tính
a) \(5\dfrac{1}{2}.3\dfrac{1}{4}\) b) \(6\dfrac{1}{3}:4\dfrac{2}{9}\) c) \(4\dfrac{3}{7}.2\)
`A=(8 2/7-4 2/7)-3 4/9`
`=8+2/7-4-2/7-3-4/9`
`=4-3-4/9`
`=1-4/9=5/9`
`B=(10 2/9-6 2/9)+2 3/5`
`=10+2/9-6-2/9+2+3/5`
`=4+2+3/5`
`=6+3/5=33/5`
Bài 2:
`a)5 1/2*3 1/4`
`=11/2*13/4`
`=143/8`
`b)6 1/3:4 2/9`
`=19/3:38/9`
`=19/3*9/38=3/2`
`c)4 3/7*2`
`=31/7*2`
`=62/7`
Bài 1:
\(A=\left(8\dfrac{2}{7}-4\dfrac{2}{7}\right)-3\dfrac{4}{9}\)
\(A=\left(\dfrac{58}{7}-\dfrac{30}{7}\right)-\dfrac{31}{9}\)
\(A=4-\dfrac{31}{9}\)
\(A=\dfrac{5}{9}\)
\(B=\left(10\dfrac{2}{9}-6\dfrac{2}{9}\right)+2\dfrac{3}{5}\)
\(B=\left(\dfrac{92}{9}-\dfrac{56}{9}\right)+\dfrac{13}{5}\)
\(B=4+\dfrac{13}{5}\)
\(B=\dfrac{33}{5}\)
Bài 2:
a) \(5\dfrac{1}{2}.3\dfrac{1}{4}=\dfrac{11}{2}.\dfrac{13}{4}=\dfrac{11.13}{2.4}=\dfrac{143}{8}\)
b) \(6\dfrac{1}{3}:4\dfrac{2}{9}=\dfrac{19}{3}:\dfrac{38}{9}=\dfrac{19}{3}.\dfrac{9}{38}=\dfrac{3}{2}\)
c) \(4\dfrac{3}{7}.2=\dfrac{31}{7}.2=\dfrac{31.2}{7}=\dfrac{62}{7}\)
\(3^{2x-1}+2.9^{x-1}=405\)
\(\left(\dfrac{1}{3}\right)^{x-1}+5.\left(\dfrac{1}{3}\right)^{x+1}=\dfrac{14}{9^3}\)
\(\dfrac{3}{5}.\left(3x^3-\dfrac{8}{9}\right)-\dfrac{1}{2}.\left(\dfrac{3}{2}-1\right)=-\dfrac{1}{4}\)
Tìm x ( Giúp với mình cần gấp )
Để giải phương trình, ta sẽ thực hiện các bước sau: Bước 1: Giải các phép tính trong phương trình. 32x^(-1) + 2.9x^(-1) = 405(13)^(-1) + 5.(13)^2 + 1 = 1493(31)^(-1) + 5.(31)^2 + 1 = 9314(35)^(-1) Bước 2: Rút gọn các số hạng. 32x^(-1) + 2.9x^(-1) = 405/13 + 5.(13)^2 + 1 = 1493/31 + 5.(31)^2 + 1 = 9314/35 Bước 3: Đưa các số hạng về cùng mẫu số. 32x^(-1) + 2.9x^(-1) = (405/13).(31/31) + 5.(13)^2 + 1 = (1493/31).(13/13) + 5.(31)^2 + 1 = 9314/35 Bước 4: Tính toán các số hạng. 32x^(-1) + 2.9x^(-1) = 405.(31)/13.(31) + 5.(13)^2 + 1 = 1493.(13)/31.(13) + 5.(31)^2 + 1 = 9314/35 Bước 5: Tính tổng các số hạng. 32x^(-1) + 2.9x^(-1) = 405.(31)/403 + 5.(13)^2 + 1 = 1493.(13)/403 + 5.(31)^2 + 1 = 9314/35 Bước 6: Đưa phương trình về dạng chuẩn. 32x^(-1) + 2.9x^(-1) - 9314/35 = 0 Bước 7: Giải phương trình. Để giải phương trình này, ta cần biến đổi nó về dạng tương đương. Nhân cả hai vế của phương trình với 35 để loại bỏ mẫu số. 35.(32x^(-1) + 2.9x^(-1) - 9314/35) = 0 1120x^(-1) + 101.5x^(-1) - 9314 = 0 Bước 8: Tìm giá trị của x. Để tìm giá trị của x, ta cần giải phương trình này. Tuy nhiên, phương trình này không thể giải được vì x có mũ là -1.