Question

in1. So sánh A và B, biết:

A=2011²⁰¹¹+2/2011²⁰¹¹-1

B=2011²⁰¹¹/2011²⁰¹¹-3

2.tính

(2¹⁷+4¹⁷)(3¹⁴-3¹²)(2⁴-4²)/1⁵²+5³

^{3.chứng tỏ rằng:}

1/2²+1/3²+1/4²+...+1/2010²<1

4. Tính a², biết:

a= 2.9.8+3.12.10+4.15.12+...+98.297.200/2.3.4+3.4.5+4.5.6+...+98.99.100

Answer 1

Bài 3:

Ta có:

\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+\(...\)+\(\frac{1}{2010^2}\)<\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+...+\(\frac{1}{2009.2010}\)

Xét:\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+.....+\(\frac{1}{2009+2010}\)=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\)=\(1-\frac{1}{2010}\)<1

\(\Rightarrow\)\(\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{2010^2}< 1\)

\(\)Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2010^2}< 1\)