a)\(\frac{1}{24}+\frac{1}{60}+\frac{1}{120}+...+\frac{1}{2184}\)
b) 1+2+2^2 + 2^3 +...+ 2^100
c) 1! + 2.2! + 3.3! +...+ 10.10!
d) 1.2 + 2.5 + 3.8 + ... + 50.149
e) 1^2 + 2^2 + 3^2 +...+ 10^2
Các bạn làm cho mk nhoa!
a) S1 = 1+2^2+2^3+......+2^20
b) S2 =1+3^2+3^3+.......+3^15
c)S3 =6+5^2+5^3+........+5^10
d)S4= 1.2+2.3+3.4+......+99.100
e)S5 = 2.2+2.5+3.8+.....+50.149
1. tính
a) A=\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
b) B=\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
c) C=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
d) D=\(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{92.98}\)
1) a) A=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{3}-\frac{1}{8}=\frac{5}{24}\)
c) C=\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)
\(C=1-\frac{1}{101}\)
\(C=\frac{100}{101}\)
d) Sửa đề: thay \(\frac{3}{92.98}\)=\(\frac{3}{92.95}\)
\(D=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{92}-\frac{1}{95}\)
\(D=\frac{1}{2}-\frac{1}{95}\)
\(D=\frac{95-2}{190}=\frac{93}{190}\)
Các bài trên áp dụng theo tính chất: \(\frac{a}{b\left(b+a\right)}\frac{1}{b}-\frac{1}{b+a}\)
Tính \(A=-\frac{19}{2^3.3^2.5}+\left(-3\frac{1}{2}\right)^2:1,2-\left(-1\frac{1}{3}\right)^3:\frac{5}{6}\)
tính tổng
\(A=\frac{1}{1.2}+\frac{2}{1.3}+\frac{3}{2.5}+\frac{5}{3.8}+\frac{8}{5.13}+\frac{13}{8.21}+...+\frac{987}{610.1597}\)
\(B=\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+...+\frac{2017^2}{2016.2018}\)
\(C=\frac{5}{1.2.3}+\frac{8}{2.3.4}+\frac{11}{3.4.5}+...+\frac{6025}{2011.2012.2013}\)
bạn phải cho ra 2 số cuối thì mới làm đc nha có 1 s
ố cuối ko làm đc đâu
A= 1-1/2 + 1-1/3 + 1/2-1/5 + 1/3-1/8+ 1/5-1/13+1/8- 1/21 +....+ 1/610- 1/1597
A= 1/610
1/610 nha bn
k giùm mk nha các bn
>_< học tốt
Thực hiện phép tính:
a) \(\frac{\left(2^3.3^3\right)^2.5^5}{\left(2^2\right).\left(3^2.5^2\right)^2}\)
b) \(\frac{2^3.11-2^3.8}{6.\left(-1\right)^{2014}}\)
1. tìm x trong các tỉ lệ thức sau
a) 3.8:(2x)= \(\frac{1}{4}\):\(2^{\frac{2}{3}}\)
b) (0,25x):3= 5/6 : 0.125
c) 0.01:2.5=(0.75x) : 0.75
d) \(1\frac{1}{3}\):0.8= 2/3: (0.1x)
a: \(\Leftrightarrow2x=\dfrac{19}{5}:\dfrac{3}{32}=\dfrac{608}{15}\)
hay x=304/15
b: \(\Leftrightarrow0.25x=20\)
hay x=80
c: \(\Leftrightarrow x=\dfrac{1}{100}:\dfrac{5}{2}=\dfrac{2}{500}=\dfrac{1}{250}\)
d: \(\Leftrightarrow0.1x=\dfrac{2}{3}:\dfrac{5}{3}=\dfrac{2}{5}\)
hay \(x=\dfrac{2}{5}:\dfrac{1}{10}=\dfrac{20}{5}=4\)
Bài : Thực hiện phép tính:
\(\left(2^2+2^1+2^2+2^3\right).2^0.2^1.2^2.2^3\)
\(1\frac{3}{8}+\frac{1}{8}:\left(0,75-\frac{1}{2}\right)-25\%.\frac{1}{2}\)
\(12\frac{1}{3}-\frac{5}{6}:\left(24-23\frac{5}{7}\right)\)
\(\left(\frac{-1}{2}\right)^2-\left(-2\right)^2-5^0\)
(22+21+22+23).20.21.22.23
=(4+2+4+8).1.2.4.8
=18.1.2.4.8
=1152
1 3/8+1/8:(0,75-1/2)-25%.1/2
=11/8+1/8:(3/4-1/2)-1/4.1/2
=12/8:1/4-1/8
=6/1-1/8
=47/8
12 1/3-5/6:(24-23 5/7)
=37/3-5/6:(24-166/7)
=37/3-5/6:2/7
=37/3-35/2
=31/6
(-1/2)2-(-2)2-50
=1/4-4-1
=-19/4
\(\left(2^2+2^1+2^2+2^3\right)×2^0×2^1×2^2×2^3\)
\(=\left(4+2+4+8\right)×1×2×4×8\)
\(=18×1×2×4×8\)
\(=1152\)
\(1\frac{3}{8}+\frac{1}{8}:\left(0,75-\frac{1}{2}\right)-25\%×\frac{1}{2}\)
\(=\frac{11}{8}+\frac{1}{8}:\left(\frac{3}{4}-\frac{1}{2}\right)-\frac{1}{4}×\frac{1}{2}\)
\(=\frac{11}{8}+\frac{1}{8}:\frac{1}{4}-\frac{1}{8}\)
\(=\frac{11}{8}+\frac{1}{2}-\frac{1}{8}\)
\(=\frac{7}{4}\)
\(12\frac{1}{3}-\frac{5}{6}:\left(24-23\frac{5}{7}\right)\)
\(=\frac{37}{3}-\frac{5}{6}:\left(24-\frac{166}{7}\right)\)
\(=\frac{37}{3}-\frac{5}{6}:\frac{2}{7}\)
\(=\frac{37}{3}-\frac{35}{12}\)
\(=\frac{113}{12}\)
\(\left(\frac{-1}{2}\right)^2-\left(-2\right)^2-5^0\)
\(=\frac{1}{4}-4-1\)
\(=\frac{-19}{4}\)
m.n giúp mk mấy câu vio 7 với:
1)Cho \(D=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+......+\frac{10}{1400}\)
\(E=\frac{1}{1+2}+\frac{1}{1+2+3}+......+\frac{1}{1+2+3+....+24}\)
Tính tỉ số D/E?
2)Giả sử \(\frac{a+b}{a+c}=\frac{a-b}{a-c}\) và a khác c;a khác -c;ac khác 0
Tính giá trị biểu thức \(A=\frac{10b^2+9bc+c^2}{2b^2+bc+2c^2}\)
1) \(D=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+....+\frac{10}{1400}\)
\(D=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+.....+\frac{5}{700}\)
\(D=\frac{5}{4.7}+\frac{5}{7.10}+\frac{5}{10.13}+......+\frac{5}{25.28}\)
\(D=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+.....+\frac{3}{25.28}\right)\)
\(D=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+....+\frac{1}{25}-\frac{1}{28}\right)\)
\(D=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}.\frac{6}{28}=\frac{5}{14}\)
\(E=\frac{1}{1+2}+\frac{1}{1+2+3}+.......+\frac{1}{1+2+3+....+24}\)
Ta có: \(1+2=\)\(\frac{2.\left(2+1\right)}{2}=3\);\(1+2+3=\frac{3.\left(3+1\right)}{2}=6\);\(1+2+3+...+24=\frac{24.\left(24+1\right)}{2}=300\)
\(E=\frac{1}{3}+\frac{1}{6}+....+\frac{1}{300}\)
=>\(\frac{1}{2}E=\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{600}=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{24.25}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{24}-\frac{1}{25}=\frac{1}{2}-\frac{1}{25}=\frac{23}{50}\)
=>\(E=\frac{46}{50}\)
Vậy \(\frac{D}{E}=\frac{5}{14}:\frac{46}{50}=\frac{250}{644}=\frac{125}{322}\)
2) Theo t/c dãy tỉ số=nhau:
\(\frac{a+b}{a+c}=\frac{a-b}{a-c}=\frac{a+b-\left(a-b\right)}{a+c-\left(a-c\right)}=\frac{a+b-a+b}{a+c-a+c}=\frac{2b}{2c}=1\)
=>b=c
do đó \(A=\frac{10b^2+9bc+c^2}{2b^2+bc+2c^2}=\frac{10b^2+9b^2+b^2}{2b^2+b^2+2b^2}=\frac{\left(10+9+1\right).b^2}{\left(2+1+2\right).b^2}=4\)
Bài 1 hãy tính
1 . A = \(\frac{9^5.5^7}{45^7}\)
2 .B = \(\left(\frac{2^2.2^3}{4^2.16}\right)^{15}\)\(:\left(\frac{2^6}{16^2}\right)^{10}\)
3 . A= \(\frac{-5.7^5+7^4}{7^6.10-2.7^5}\)
4 . B = \(\frac{10^3+5.10^2.5^3}{-13}\)
5 . A = \(\frac{\left(-0,03\right)^7.2^8}{\left(0,6\right)^7}\)
6 . B= \(\frac{3^7.16^3}{12^5.27^2}\)
7 . A = \(\frac{2^3.\left(0,5\right)^3.3^7}{2.\left(,5\right)^4.3^8}\)
8 . B = \(\left(\frac{-1}{3}\right)^3\)\(.\left(\frac{-1}{3}\right)^2\)\(.\left(\frac{-1}{3}\right)\)
Giúp mik nhé . mik cần ngay