Cho:P =(1-1/1+2)(1-1/1+2+3)(1-1/1+2+3+4)...(1-1/1+2+3+...+2014). Tính: 2014/2016P
TN
Những câu hỏi liên quan
Tính:
A= 2014 + \(\frac{2014}{1+2}+\frac{2014}{1+2+3}+\frac{2014}{1+2+3+4}+........+\frac{2014}{1+2+3+4+.....+2013}\)
\(A=2014.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+2013}\right)\)
\(A=2014.\left(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{1007.2013}\right)\)
\(A=2.2014.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{2013.2014}\right)\)
\(A=2.2014.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2013.2014}\right)\)
\(A=2.2014.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}\right)\)
\(A=2.2014.\left(1-\frac{1}{2014}\right)\)
\(A=2.2014.\frac{2013}{2014}\)
\(A=\frac{2.2014.2013}{2014}\)
\(A=2.2013\)
\(A=4026\)
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NV
27 tháng 2 2022 lúc 10:22
1*2*3*...*2015-1*2*3*4*...*2014-1*2*3*...*2013*2014^2 tính nhanh
\(1.2.3....2015-1.2.3....2014-1.2.3....2013.2014^2\)
\(=1.2.3...\left(2014+1\right)-1.2.3...\left(2014+1\right)\)
\(=0\)
bạn làm thế là sai rồi
có 3 con 2014 cơ mà
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Tính tổng \(S=2014+\frac{2014}{1+2}+\frac{2014}{1+2+3}+\frac{2014}{1+2+3+4}\)\(+...+\frac{2014}{1+2+3+...+10000}\)
\(S=2014+\frac{2014}{1+2}+\frac{2014}{1+2+3}+...+\frac{2014}{1+2+3+...+10000}\)
\(S=\frac{2014}{\frac{1.2}{2}}+\frac{2014}{\frac{2.3}{2}}+\frac{2014}{\frac{3.4}{2}}+...+\frac{2014}{\frac{10000.10001}{2}}\)
\(S=\frac{4028}{1.2}+\frac{4028}{2.3}+\frac{4028}{3.4}+...+\frac{4028}{10000.10001}\)
\(S=4028\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10000.10001}\right)\)
\(S=4028\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{10001-10000}{10000.10001}\right)\)
\(S=4028\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10000}-\frac{1}{10001}\right)\)
\(S=4028\left(1-\frac{1}{10001}\right)=\frac{40280000}{10001}\)
A=2014+[2014:(1+2)]+[2014:(1+2+3)]+[2014:(1+2+3+4)]+...++[2014:(1+2+3+...+2013)]
rut gon bieu thuc
1/(1^4+1^2+1)+2/(2^4+2^2+1)+3/(3^4+3^2+1)+...+2014/(2014^4+2014^2+2014)=...
{giup minh vs}
1) 1/2 + 1/3 + 1/4 + ... + 1/2013 + 1/2014
2) 2014 + 2013/2 + 2012/3 + 2011/4 + ... + 2/2013 + 1/2014
Cho A= 1/2+1/3+1/4+..+1/2016
B= 2015/1+2014/2+2013/3+....+2/2014+1/2015. Tính B/A
Thực hiện tính :
a) A = 1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+...+1/2013(1+2+3+..+2013)
b) B = 1-3/7.3+2-4/2.4+3-5/3.5+4-6/4.6+....+2011-2013/2011.2013+2012-2014/2012.2014-2013+2014/2013.2014
Tính \(M=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+...+\frac{1}{2014}.\left(1+2+3+...+2014\right)\)
Lời giải:
$M=1+\frac{1}{2}.\frac{2(2+1)}{2}+\frac{1}{3}.\frac{3(3+1)}{2}+\frac{1}{4}.\frac{4(4+1)}{2}+....+\frac{1}{2014}.\frac{2014(2014+1)}{2}$
$=1+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{2015}{2}$
$=\frac{2+3+4+....+2015}{2}$
$=\frac{1+2+3+....+2015}{2}-\frac{1}{2}$
$=\frac{2015(2015+1)}{4}-\frac{1}{2}=\frac{2031119}{2}$
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