[ 5*4 ] 
Cafe IV. Given a , />, n\ Required r. 
Since A — i X a = Apr. 
Therefore L — = = 
na A nr nr nr 
Now,i +> 1 —i-nr-\-n x ——r~-—?i x V * — — r 3 
2 2 2 
&C, 
Therefore — = i — ^ x r l , nearly. 
2 2 3 y 
2 _ 2 
Then 3‘ "+■ = i-I+fr+^x^r^' , 
n a] 2 2 3 1 3 
which, by the Binomial Theorem, will become 
= i + r — lL_Irr, nearly. 
2 2 
Now, JQ ,:+ ' = 
! . 
na j 
2 
P 
Let G = (yp 
=) 
, » — r 2 
i -4- r r . 
1 12 
Therefore rr — 
12 
X 
M 
1 
0 
1 
II 
V, 
1 
n — 
i 
Let 2 H — 12 
I * 
Then r — H = (Vh~2.G— i x H =)k. 
Therefore r == H — K. 
Cafe V. Given a, n , r j Required 
Since A — i x ~tnr. Therefore m — A ~ h — 
Cafe VI. 
