Tính \(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{2018}\left(1+2+3+...+2018\right)\)
Những câu hỏi liên quan
Thực hiện phép tính:\(\left(1-\frac{1}{2018}\right).\left(1-\frac{2}{2018}\right).\left(1-\frac{3}{2018}\right)...\left(1-\frac{2020}{2018}\right)\)
â , tính M = \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right).......\left(1+\frac{1}{2017}\right)\left(1+\frac{1}{2018}\right)\)
b , Cho A = \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2017}-\frac{1}{2018}\)
c , B = \(\frac{1}{1010}+\frac{1}{1011}+.....+\frac{1}{2017}+\frac{1}{2018}.tinh\left(\frac{A}{B}\right)^{2018}\)
a, \(M=\frac{3}{2}\cdot\frac{4}{3}\cdot\cdot\cdot\cdot\frac{2018}{2017}\cdot\frac{2019}{2018}=\frac{3.4...2019}{2.3...2018}=\frac{2019}{2}\)
b, c cùng 1 câu phải k
ta có: \(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2017}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2018}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2018}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2018}\right)\)
\(=1+\frac{1}{2}+...+\frac{1}{2018}-\left(1+\frac{1}{2}+...+\frac{1}{1009}\right)\)
\(=\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2018}=B\)
\(\Rightarrow\frac{A}{B}=1\Rightarrow\left(\frac{A}{B}\right)^{2018}=1^{2018}=1\)
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A,\(M=\frac{3}{2}\cdot\frac{4}{3}....\frac{2018}{2017}\cdot\frac{2019}{2018}=\frac{4\cdot3...2019}{2\cdot3...2018}=\frac{2019}{2}\)
NHA
HỌC TỐT
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\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{2018}\left(1+2+3+...+2018\right)\)
Tính :
a) \(\text{A}=\left(1\times2\right)^{-1}+\left(2\times3\right)^{-1}+...+\left(2014\times2015\right)^{-1}\).
b) \(\text{B}=\frac{2018+\frac{2017}{2}+\frac{2016}{3}+\frac{2015}{4}+...+\frac{2}{2017}+\frac{1}{2018}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2018}+\frac{1}{2019}}\).
Thực hiện phép tính:a, A frac{1}{6}.left(-2frac{3}{5}right)+1frac{2}{3}.left(frac{-13}{5}right)b, Bfrac{5}{7}:left(frac{1}{2}-frac{1}{3}right)+frac{5}{7}:left(frac{1}{5}-frac{1}{6}right)c, C 2^3+3.left(frac{2017}{2018}right)^0.left(frac{1}{2}right)^{-2}:4+[left(-2right)^2:frac{1}{2}].left(frac{-1}{2}right)^3giúp vs, mik cần gấp
Đọc tiếp
Thực hiện phép tính:
a, A= \(\frac{1}{6}.\left(-2\frac{3}{5}\right)+1\frac{2}{3}.\left(\frac{-13}{5}\right)\)
b, B=\(\frac{5}{7}:\left(\frac{1}{2}-\frac{1}{3}\right)+\frac{5}{7}:\left(\frac{1}{5}-\frac{1}{6}\right)\)
c, C= \(2^3+3.\left(\frac{2017}{2018}\right)^0.\left(\frac{1}{2}\right)^{-2}:4+[\left(-2\right)^2:\frac{1}{2}].\left(\frac{-1}{2}\right)^3\)
giúp vs, mik cần gấp
A= E387E4837
B = 883433
C = UỲUWFHQWURY48E3947
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Thực hiện phép tính : \(\left(1\frac{1}{1+2}\right).\left(1\frac{1}{1+2+3}\right)...\left(1\frac{1}{1+2+3+...+2018}\right)\)
Thực hiện phép tính
\(\left(1-\frac{1}{1+2}\right).\left(1-\frac{1}{1+2+3}\right)...\left(1-\frac{1}{1+2+3+...+2018}\right)\)
Tính:\(\left(2018-\frac{1}{3}-\frac{2}{4}-\frac{3}{5}-...-\frac{2018}{2020}\right):\left(\frac{1}{15}+\frac{1}{20}+\frac{1}{25}+...+\frac{1}{10100}\right)\)
nhanh nha mấy bạn mình đang cần rất gấp
1, Tính giá trị biểu thức :
\(a,A=5\frac{9}{10}:\frac{3}{2}-\left(2\frac{1}{3}.4\frac{1}{2}-2.2\frac{1}{3}\right):\frac{7}{4}\)
\(b,B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).............\left(1-\frac{1}{2017}\right).\left(1-\frac{1}{2018}\right)\)
Mọi người giúp mình giả toán nha !
Ta có:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)........\left(1-\frac{1}{2017}\right).\left(1-\frac{1}{2018}\right)\)
\(\Rightarrow B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{2016}{2017}.\frac{2017}{2018}\)
Đởn giản hết sẽ còn là:
\(\Rightarrow B=\frac{1}{2018}\)
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