tính giá trị biểu thức B=3/(1*2)^2+5/(2*3)^2+...+61/(30*31)^2
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Có:
\(a+b+c=0\\\Leftrightarrow\left(a+b+c\right)^2=0\\ \Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca=0\\ \Leftrightarrow2ab+2bc+2ca=-1\\ \Leftrightarrow ab+bc+ca=-\dfrac{1}{2}\\ \Leftrightarrow\left(ab+bc+ca\right)^2=\left(-\dfrac{1}{2}\right)^2=\dfrac{1}{4}\\ \Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2a^2bc+2ab^2c+2abc^2=\dfrac{1}{4}\\ \Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)=\dfrac{1}{4}\\ \Leftrightarrow a^2b^2+b^2c^2+c^2a^2=\dfrac{1}{4}-0=\dfrac{1}{4} \)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1)
a) - 37 + 54 + (- 70) + (-163) + 246
= (-37 + (-163)) + (54 + 246) + (-163)
= -200 + 300 + (- 163)
= 100 + (-163)
= - 63
b) 125. (-61) . 23. (-1)2n
= (125 . 23) . (-61) . 1
= 1000 . (- 61)
= - 6100
c) mk không biết làm nha
a)-37+54+-70+-163+246
=[(-370 + (-70)+(-163)]+(54 + 246)
=(-603)+300
=-303
c)1+2-3-4+5+6 -7....+2014-2015-2016+2017+2018
=-4+-4+......+-4+2018
=(-4).505+2018
=-2020+2018
=-2
![](https://rs.olm.vn/images/avt/0.png?1311)
x^2*(x-30)-31x+1
thay x=31 vao bieu thuc
(31)^2*(31-30)-31*31+1=1
\(B=\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+\frac{7}{\left(3.4\right)^2}+....+\frac{61}{\left(30.31\right)^2}\)
\(=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{61}{30^2.31^2}\)
\(=\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+\frac{4^2-3^2}{3^2.4^2}+...+\frac{31^2-30^2}{30^2.31^2}\)
\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+....+\frac{1}{30^2}-\frac{1}{30^2}\)
\(=1-\frac{1}{31^2}=1-\frac{1}{961}=\frac{960}{961}\)