Rasyonel Sayilar

Question

A=4/100+4/1000+4/10000+4/100000+... 

sayisina hangisi eklenirse sonuc bir tam sayi olur?

Answer 1

$A=\dfrac{4}{100}+\dfrac{4}{1000}+\dfrac{4}{10000}+\dfrac{4}{100000}+ \dots= \\ = 0,04+0,004+0,0004+0,0004+\dots=0,0\bar{4}=\dfrac{4}{90} \\ B (\in Z)=A+C=\dfrac{4}{90}+\dfrac{86}{90} \\ C=\dfrac{43}{45}=0,\overline{86}$