tinh \(1+1+2.15+1+3\left(23456.7968798.\left(234233-234233\right)\right)\)
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\(VT=\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+...+\frac{1}{\left(x+3\right)\left(x+4\right)}\)
\(=\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+...+\frac{1}{x+3}-\frac{1}{x+4}\)
\(=\frac{1}{x}-\frac{1}{x+4}=\frac{x+4-x}{x\left(x+4\right)}=\frac{4}{x\left(x+4\right)}\)
\(\Rightarrow\frac{4}{x\left(x+4\right)}=\frac{m}{x\left(x+4\right)}=VP\Rightarrow m=4\)

B=\(\dfrac{1}{\left|x-2\right|+3}\)
do \(\left|x-2\right|\ge0\forall x\)
=> \(\left|x-2\right|+3\ge3\)
=> \(\dfrac{1}{\left|x-2\right|+3}\le\dfrac{1}{3}\)
=> B \(\le\dfrac{1}{3}\)
GTLN của B =\(\dfrac{1}{3}\)
khi x-2=0
=> x=2
vậy GTLN của A=\(\dfrac{1}{3}\) khi x=2

(1-1/3)x(1-1/5)x(1-1/7)x(1-1/9)x(1-1/2)x(1-1/4)x(1-1/6)x(1-1/8)x(1-1/10)
=2/3x4/5x6/7x8/9x1/2x3/4x5/6x7/8x9/10
=2x4x6x8x1x3x5x7x9 /3x5x7x9x2x4x6x8x10
=1/10


\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{100}\right)\)
=\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{99}{100}\)
=\(\frac{1.2.3...99}{2.3.4...100}\)
=\(\frac{1}{100}\)
Chúc bạn học giỏi nha


\(\left(\frac{1}{2}a+b\right)^3+\left(\frac{1}{2}a-b\right)^3\)
\(=\left(\frac{a}{2}\right)^3+3\times\left(\frac{a}{2}\right)^2b+3\times\frac{a}{2}b^2+b^3+\left(\frac{a}{2}\right)^3-3\times\left(\frac{a}{2}\right)^2b+3\times\frac{a}{2}b^2+b^3\)
\(=\frac{a^3}{8}+3\times\frac{a^2}{4}b+3\times\frac{a}{2}b^2+b^3+\frac{a^3}{8}-3\times\frac{a^2}{4}b+3\times\frac{a}{2}b^2+b^3\)
\(=\left(\frac{a^3}{8}+\frac{a^3}{8}\right)+\left(\frac{3a^2b}{4}-\frac{3a^2b}{4}\right)+\left(\frac{3ab^2}{2}+\frac{3ab^2}{2}\right)+\left(b^3+b^3\right)\)
\(=\frac{a^3}{4}+3ab^2+2b^3\)
1+1+2.15+1+3(23456.7968798.(234233-234233))
=2+30+1+3(23456.7968798.0)
=33+3.0
=33
1+1+2.15+1+3(23456.7968798.(234233-234233))
=2+30+1+3(23456.7968798.0)
=33+3.0
=33