Đáp án+Giải thích các bước giải:
$a)\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{47.49}=\dfrac{1}{x}$
$⇒\dfrac{1}{2(1/1-1/3)}+\dfrac{1}{2(1/3-1/5)}+...+\dfrac{1}{2(1/47-1/49)}=\dfrac{1}{x}$
$⇒\dfrac{1}{2(1-1/3+1/3-1/5+...+1/47-1/49)}=\dfrac{1}{x}$
$⇒\dfrac{1}{2(1-1/49)}=\dfrac{1}{x}$
$⇒\dfrac{1}{2.48/49}=\dfrac{1}{x}$
$⇒\dfrac{24}{49}=\dfrac{1}{x}$
$⇒24x=49$
$⇒x=\dfrac{49}{24}$
$b)1/1.4+1/4.7+...+1/97.100=2/x$
$⇒1/3(1/1-1/4)+1/3(1/4-1/7)+...+1/3(1/97-1/100)=2/x$
$⇒1/3(1-1/4+1/4-1/7+...+1/97-1/100)=2/x$
$⇒1/3(1-1/100)=2/x$
$⇒1/3.99/100=2/x$
$⇒33/100=2/x$
$⇒33x=200$
$⇒x=200/33$
$c)4/1.5+4/5.9+..+4/97/101=2x+5/101$
$⇒4(1/1.5+1/5.9+...+1/97.101)=2x+5/101$
$⇒4[1/4(1-1/5)+1/4(1/5-1/9)+...+1/4(1/97-1/101)]=2x+5/101$
$⇒4.1/4(1-1/5+1/5-1/9+...+1/97-1/101)=2x+5/101$
$⇒-1/101=2x+5/101$
$⇒-1=2x+5$
$⇒2x=-6$
$⇒x=-3$
$d)(1-1/2)(1-1/3).....(1-1/100)+x=2 1/5$
$⇒1/2.2/3.....99/100+x=11/5$
$⇒1/100-11/5=-x$
$⇒1/100-220/100=-x$
$⇒-219/100=-x$
$⇒x=219/100$
