104, Mr. Woodhouse on the Truth of Conclusions 
. P — (« + 0 v/“ — X s/~i 
e — x ^ — 1 _ j 
(« + 0 X V— J __ g x 
„ X s/zz\ 
Hence the series is represented 
; )+^ 
, e — (»'+' 0 ? S / ~ i _ e — x \/—\ 
e x v/— 1 — i 
which is the same as 
e (« + \) x'Z—x _ gX \/—\ e — x s / — i j (n + \) —\__ e —xV — i 
X — X 7-= hi 
vd~T 
X V I ! 
e x ^ i — I 
x — , or is 
V~ 
(n + x) x S/— i + e x \/ 
2,? — e x ^ i + e x ^ 1 
+ 2 x 
g — n x \/ — i t g — (n -J- x) sc \/- 
— x s/ - 
nx\/— ij_>— i \ + -(«+iW-i j _ ( e xK/ ~ l x-e— vS/r ~~ 
+ 
+ * 
2 X \ 1 — 
:* I + g — * %/ ~ 1 
cos. n x — cos. (n + i) x - f cos, x — i 
2 x ( i — cos. x ) 
In like manner, the series sin. x -f- sin. 2 x + . . . sin, m x may 
i i sin. x — sin, (in + i ) x + sin. m x T i -. 
be shewn = T ^T— l oT.T) • -*• he sum ot cos * x 
+ cos. 22: ... cos. nx may easily be found, by expressing it 
Ix^—i — xV'— l \ j 
under the form [ j + ( 
( nx _ n x v/— 1 \ 
i - — — j ; which, by expanding the terms, 
