48 BOOK OF MATHEMATICAL PROBLEMS. 



. . 4* 



+1+ nx 



tf ^ 



" f+ ~ 



(11) I 1 A J"'- 1 )' - = !L 

 ' 1-5-13-.. .-n' + (+l)- 



2 3 8 n'-l _n( + 8) 



' i_5-7-.. .-2w + l- 2 



1-3-4-5-.. .-w + 2-... to oo 



= -!, 



r 2r 3r 

 + __7T3-^Tl-... to oo ~ 







.,_ x rr + lr4-2 r-1 



(17) - to oo = _ . 



; r-r+ I-r + '2-... r-2 



214. The numerator and denominator of any convergent to 

 the fraction --^- -^y ^y differ from each other by 

 unity. 



tn rp if If 



215. If - " be the n th convergent to - =- 



fj 1^ j__|_y-|_j^^-^_j[^. t>i 



then will 



