Page 110 - Милогия 2001-full

n ( n + 1) , n = 1, 2 , 3, ...
2

n ( n + 1)( n + 2 ) , n = 1, 2 , 3, ...
6

( n n - 1)
n + (k - 2) , n = 1, 2, 3, ...
2

¥ ¥ - n ( n- - 1)...( n- - r + 1)
r
r
-
-
(1 - ) x - n = å ( )( x ) = å ( x ) =
-
n
r
r = 0 r = 0 ! r
¥ ( n + r - 1)...( n + 1) n ¥
= å x r = å ( r n + - 1 )x r
r
r = 0 ! r r = 0
( ) ( )
n r+
1 -
-
=
n
r
r
n
P ( x = ( 1 + x + ...+ x m - 1 n = ( ) x r
)
)
r
m
n-
n-
n-
( ) ( ) ( ) + + ( r m- + )
+
=
1
1
1
n
...
r
m r m r- 1 m 1 m
( ) m
n
r
(1 + ) 1 n = ( ) , r = 0,n
n
r
2
n
n
(1 + 1 + 1 ) = ( ) , r = 0,n
r
3