Question

So sánh A và B:

1. A=\(\dfrac{79^{2011} - 5}{79^{2011} + 8}\) và B=\(\dfrac{79^{2012} - 6}{79^{2011} + 7}\)

2. A=\(\dfrac{43}{2011^{2012}}\)+\(\dfrac{79}{2011^{2013}}\) và B=\(\dfrac{79}{2011^{2012}}\)+\(\dfrac{43}{2011^{2013}}\)

3. A=\(\dfrac{2010}{2011}\):\(\dfrac{2011}{2012}\) và B=\(\dfrac{2010+2011}{2011+2012}\)

4. A=\(\dfrac{n}{2n+1}\) và B=\(\dfrac{3n+1}{6n+3}\)

Thanks mấy bạn trước nha!!

Answer 1

2.A=\(\dfrac{43.11}{2011^{2013}}\)+\(\dfrac{79}{2011^{2013}}\)=\(\dfrac{43.11+79}{2011^{2013}}\)

B=\(\dfrac{79.11}{2011^{2013}}\)+\(\dfrac{43}{2011^{2013}}\)=\(\dfrac{79.11+43}{2011^{2013}}\)

Ta có: 43.11+79=43.(10+1)+79=43.10+43+79=430+122

79.11+43=79.(10+1)+43=79.10+79+43=790+122

Vì 430+122<790+122 nên 43.11+79<79.11+43 (1)

Mà 2011²⁰¹³<2011²⁰¹³ (2)

Từ (1) và (2) suy ra A<B

Answer 2

3. A=\(\dfrac{2010.2012}{2011.2011}\)

Vì B<1 nên B>\(\dfrac{2010}{2012}\)=\(\dfrac{2010.2012}{2012.2012}\)

Vì 2010.2012=2010.2012; 2011.2011<2012.2012 nên B>A

4. A=\(\dfrac{3n}{3\left(2n+1\right)}\)=\(\dfrac{3n}{6n+3}\)

Vì 6n+3=6n+3; 3n<3n+1 nên A<B