Question

Tìm x, biết:

a) \(\frac{29}{30}\)-\((\frac{13}{23}\)+x\()\)=\(\frac{7}{69}\)

b) \(\frac{1}{2}\)+\(\frac{1}{6}\)+\(\frac{1}{12}\)+...+\(\frac{1}{x\left(x+1\right)}\)=\(\frac{2011}{2012}\)

Answer 1

a) \(\frac{29}{30}\)- (\(\frac{13}{23}\)+X)=\(\frac{7}{69}\)

\(\frac{13}{23}\)+X=\(\frac{29}{30}\)-\(\frac{7}{69}\)

\(\frac{13}{23}\)+X=\(\frac{199}{230}\)

X=\(\frac{199}{230}\)-\(\frac{13}{23}\)

X=\(\frac{3}{10}\)

b)1/2+1/6+1/12+...+1/x(x+1)=2011/2012

=>1/1.2+1/2.3+1/3.4+...+1/x(x+1)=2011/2012

=>1-1/2+1/2-1/3+1/3+1/4+...+1/x+1/x+1=2011/2012

=>1-1/x+1=2011/2012

=>1/x+1=1-2011-2012

=>1/x+1=2012/2012-2011/2012

1/x+1=1/2012

=>x+1=2012

=>x=2011

Answer 2

a) 3/10