Question

cho B=12/(2x4)^2+20/(4x6)^2+...+388/(96x98)^2+396/(98x100)^2

hãy so sánh B và 1/4

mình đang cần gấp ai nhanh mình tick cho.....

 

 

Answer 1

B=\(\frac{12}{\left(2.4\right)^2}\)+\(\frac{20}{\left(4.6\right)^2}\)+.....+\(\frac{396}{\left(98.100\right)^2}\)

B=\(\frac{4^2-2^2}{2^2.4^2}\)+ \(\frac{6^2-4^2}{4^2.6^2}\)+....+\(\frac{100^2-98^2}{\left(98^2.100^2\right)}\)

B=\(\frac{1}{2^2}\)-\(\frac{1}{4^2}\)+\(\frac{1}{4^2}\)-\(\frac{1}{6^2}\)+....+\(\frac{1}{98^2}\)-\(\frac{1}{100^2}\)

B=\(\frac{1}{2^2}\)-\(\frac{1}{100^2}\)< \(\frac{1}{2^2}\)=\(\frac{1}{4}\)

Vậy B<\(\frac{1}{4}\)

Answer 2

B<\(\frac{1}{4}\)