Tính \(B=-\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+...+\frac{4}{5^{200}}\)
Tính
A = \(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)
B = \(\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+...+\frac{4}{5^{200}}\)
A=\(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)
\(\Rightarrow7A=(1+\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{99}})-\left(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+....+\frac{1}{7^{100}}\right)\)
\(\Rightarrow6A=\left(1-\frac{1}{7^{99}}\right)\)
\(\Rightarrow A=\left(1-\frac{1}{7^{99}}\right):6\)
Câu b tương tự nha
a) \(A=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...........+\frac{1}{7^{100}}\)
\(\Rightarrow7A=1+\frac{1}{7}+\frac{1}{7^2}+.........+\frac{1}{7^{99}}\)
\(\Rightarrow7A-A=6A=1-\frac{1}{7^{100}}\)
\(\Rightarrow A=\frac{1-\frac{1}{7^{100}}}{6}\)
\(A=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)
\(\frac{A}{7}=\frac{1}{7^2}+\frac{1}{7^3}+\frac{1}{7^4}+...+\frac{1}{7^{101}}\)
\(A-\frac{A}{7}=\left(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\right)-\left(\frac{1}{7^2}+\frac{1}{7^3}+\frac{1}{7^4}+...+\frac{1}{7^{101}}\right)\)
\(\frac{6}{7}A=\frac{1}{7}-\frac{1}{7^{101}}\)
\(A=\left(\frac{1}{7}-\frac{1}{7^{101}}\right).\frac{7}{6}\)
\(A=\frac{1}{6}-\frac{1}{6.7^{100}}\)
\(B=\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+...+\frac{4}{5^{200}}\)
\(=4.\left(\frac{1}{5}+\frac{1}{5^2}-\frac{1}{5^3}+...+\frac{1}{5^{200}}\right)\)
Gọi \(C=\frac{1}{5}+\frac{1}{5^2}-\frac{1}{5^3}+...+\frac{1}{5^{200}}\)
\(\frac{C}{5}=\frac{1}{5^2}+\frac{1}{5^3}-\frac{1}{5^4}+...+\frac{1}{5^{201}}\)
\(C-\frac{5}{C}=\left(\frac{1}{5}+\frac{1}{5^2}-\frac{1}{5^3}+...+\frac{1}{5^{200}}\right)-\left(\frac{1}{5^2}+\frac{1}{5^3}-\frac{1}{5^4}+...+\frac{1}{5^{201}}\right)\)
\(\frac{4}{5}C=\frac{1}{5}-\frac{1}{5^{201}}\)
\(C=\left(\frac{1}{5}-\frac{1}{5^{201}}\right).\frac{5}{4}\)
\(=\frac{1}{4}-\frac{1}{4.5^{200}}\)
Thay vào B ta có
\(B=4.\left(\frac{1}{4}-\frac{1}{4.5^{200}}\right)\)
=\(=1-\frac{1}{5^{200}}\)
Tính các tổng sau:
a) \(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}.\)
b) \(-\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+...+\frac{4}{5^{200}}.\)
c)\(\frac{-1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{100}}-\frac{1}{3^{101}}\)
Đăt A = \(\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+......+\frac{1}{7^{100}}\)
\(\Rightarrow7A=1+\frac{1}{7}+\frac{1}{7^2}+.....+\frac{1}{7^{100}}\)
\(\Rightarrow7A-A=1-\frac{1}{7^{100}}\)
\(\Rightarrow6A=1-\frac{1}{7^{100}}\)
\(\Rightarrow A=\frac{1-\frac{1}{7^{100}}}{6}\)
Tính các tổng sau
\(A=7-7^4+7^7-...+7^{301}\)
\(B=\frac{1}{7}+\frac{1}{7^2}+\frac{1}{7^3}+...+\frac{1}{7^{100}}\)
\(C=\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+...+\frac{4}{5^{200}}\)
AI TÍNH ĐƯỢC MÌNH CHO 10 TICK NHA
Tính tổng:
B= - \(\frac{4}{5}\)+\(\frac{4}{5^2}\)-\(\frac{4}{5^3}\)+....+\(\frac{4}{5^{200}}\)
Ai nhanh mk tặng 3 tick. Giúp mk vs
B=-4/5+4/52-4/53+...+4/5200
5B=-4+4/5-4/52+...+4/5201
5B+B=-4+4/5200
6B=-4x5200/5200+4/5200
6B=-4+4x5200/5200
Còn lại bạn tính nốt nha
Rút gọn biểu thức sau
B = 1 + \(\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+...+\frac{200}{2^{200}}\)
\(B=1+\frac{3}{2^3}+\frac{4}{2^4}+...+\frac{200}{2^{200}}\)
\(2B=2\left(1+\frac{3}{2^3}+\frac{4}{2^4}+...+\frac{200}{2^{200}}\right)\)
\(2B=2+\frac{3}{2^2}+\frac{4}{2^3}+...+\frac{200}{2^{199}}\)
\(2B-B=\left(2+\frac{3}{2^2}+...+\frac{200}{2^{199}}\right)-\left(1+\frac{3}{2^3}+...+\frac{200}{2^{200}}\right)\)
.... đặt A=... giiả tiếp
B = - \(\frac{4}{5}\)+\(\frac{4}{5^2}\)-\(\frac{4}{5^3}\)+.... - \(\frac{4}{5^{199}}\)+\(\frac{4}{5^{200}}\)
B =?
Tính giá trị của biểu thức.
a) \(\left( {\frac{{ - 2}}{{ - 5}}:\frac{3}{{ - 4}}} \right).\frac{4}{5}\)
b) \(\frac{{ - 3}}{{ - 4}}:\left( {\frac{7}{{ - 5}}.\frac{{ - 3}}{2}} \right)\)
c) \(\frac{{ - 1}}{9}.\frac{{ - 3}}{5} + \frac{5}{{ - 6}}.\frac{{ - 3}}{5} + \frac{5}{2}.\frac{{ - 3}}{5}.\)
a)
\(\begin{array}{l}\left( {\frac{{ - 2}}{{ - 5}}:\frac{3}{{ - 4}}} \right).\frac{4}{5} = \left( {\frac{2}{5}.\frac{{ - 4}}{3}} \right).\frac{4}{5}\\ = \frac{{ - 8}}{{15}}.\frac{4}{5} = \frac{{ - 32}}{{75}}\end{array}\)
b)
\(\begin{array}{l}\frac{{ - 3}}{{ - 4}}:\left( {\frac{7}{{ - 5}}.\frac{{ - 3}}{2}} \right) = \frac{3}{4}:\frac{{ - 21}}{{ - 10}}\\ = \frac{3}{4}.\frac{{10}}{{21}} = \frac{{30}}{{84}} = \frac{5}{14}\end{array}\)
c)
\(\begin{array}{l}\frac{{ - 1}}{9}.\frac{{ - 3}}{5} + \frac{5}{{ - 6}}.\frac{{ - 3}}{5} + \frac{5}{2}.\frac{{ - 3}}{5}.\\ = \frac{{ - 3}}{5}.\left( {\frac{{ - 1}}{9} + \frac{5}{{ - 6}} + \frac{5}{2}} \right)\\ = \frac{{ - 3}}{5}.\left( {\frac{{ - 2}}{{18}} + \frac{{ - 15}}{{18}} + \frac{{45}}{{18}}} \right)\\ = \frac{{ - 3}}{5}.\frac{{28}}{{18}}\\ = \frac{{ - 3}}{5}.\frac{{14}}{9}\\ = \frac{{ - 14}}{{15}}\end{array}\)
1 Tính
A = 1+52+54+....................+5200 , B = 3-32+33-34+.....................+399-3100
C = \(\frac{1}{7}+\frac{1}{7^2}+.................+\frac{1}{7^{100}}\)
D = \(-\frac{4}{5}+\frac{4}{5^2}-\frac{4}{5^3}+..................+\frac{4}{5^{200}}\)
E = 63+64+..............................+6150
1/ Tìm x :
\(\frac{x\times2+5}{x+5}=\frac{6}{4}\)
2/ Tính nhanh :
a) \(\frac{4}{1\times5}+\frac{4}{5\times9}+\frac{4}{9\times13}+\frac{4}{13\times17}+\frac{4}{17\times21}\)
b) \(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times.......\times\left(1-\frac{1}{2017}\right)\)
c) \(A=2000-5-5-5-.......-5\)( có 200 số 5 )
2/
a) \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}+\frac{4}{17\cdot21}\)
\(=\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+....+\frac{1}{17}-\frac{1}{21}\right)\)
\(=1-\frac{1}{21}=\frac{20}{21}\)
b) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{2017}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot..\cdot\frac{2016}{2017}\)
\(=\frac{1}{2017}\)
c) \(A=2000-5-5-5-..-5\)(có 200 số 5)
\(A=2000-\left(5\cdot200\right)\)
\(A=2000-1000\)
\(A=1000\)