Series. 



189 



12. Examples. Determine whether the following infinite 

 series are convergent or divergent : 



I. i + '+',,+ \+ . . . 

 2 3' 4^ 



I" 2^ ^^ 



|2 I3 l4 



-V X' .1""' 



iH h -+ ,+ . . . when .v<i, 



2 3- 4^ 



If !3 14 



5. '- 1 +"i - : + 



X x-\-a x-f-2a -i-j-3^ 



when r-Ci. 

 .... when X and a are 



positive. 

 6. 



X X- X' .n 



h -f- + + . . . when .v<i, 



1.2 2.3 3.4 4.5 



^' XV (x+ij(y^iy (x-{-2)(y-^2) (x+fXy^^) 

 Avhen -V and r are positive quantities. 



.V . X- X^ , A"* 



^. 4- H A ^+ . . .when.r<i. 



1.2 3.4 5.6 7.8 



2' V 4' 



4 



\|2"^%|3"^V4"^W5 



+ 



I 2- 3- 4- 

 I 2^ V 



12. i4-~,4--^+^\4. . . . 



2- 3^ 4"^ 



.V X' .1-* 



/?. vShow that i4--^-|- -+ , + , 



1 2 1.3 1 4 



'J 



for all values of x. 



14. Show that 1+ ^ + ^ H-- + . 

 234 



all values of x. 



is convergent 



is convergent or 



