44 BOOK OF MATHEMATICAL PROBLEMS. 



202. The w th convergent to - 



^ + A 4- J + . . , 





203. If be the r& th convergent to the infinite continued 



2 



fraction - - - ; p , q will be coefficients of x n ~ l and a;" 

 a-f a+ a + ...' * H ln 



respectively in the expansion of _ 2 . 



204. Prove that, <-* being the w th convergent to the infinite 



* if 1 l" 1 1 



continued fraction - , 



a+ b + a+ b + ... 



Pn + * ~( 2+ ab )Pn + P.-, = 0, q n+e - (2 + ab) q n + ^ n _ 2 = 0. 



205. Prove that the products of the infinite continued frac- 

 tions 



1111 111 



(1) - r - - , C + y , 



a+b + c + a+... b + a + c+... 



(2} - - - - - d ^ l - l 



' w ^ a+ b + c + d a + ... ' c + 6 + a + d+ ... ' 



71 x 1 + be /n . 



are, (1) ^ -- r, (2) - r- 



7 1 + ab ' ' a + c + abc 



206. Prove that the differences of the infinite continued frac- 

 tions 



ID 1 1 i 1 111- 1 



\' a + b + c + a+...' c + b + a+ c + ... ' 



m - x x - i 1 A I i i 



*' a+ 6 + c + d + a+ ... ' c + b + a + d+ c + ... ' 



I+ab* a + c + abc' 



