TEOREMA DEL BINOMIO EJERCICIOS RESUELTOS 1. Los

!" !
$
#
%&' # %
(
∈
)
*+
- .
-, . =
-/.
-
+
−
+
.=
$
.
- .
!% 3 +
.
- . = -,+ . =
0.
- −/ . = - −+ . =
%.
-
1/
2
. = - /1+/ . =
- .
- −/ .
%3
−,
%.
-
1/
2
.
*
-, . =
⋅ =
− − −
- . =
/
1 /−/
2
1/
/
. = −
4
!%
. - . =
& % +
,
* % !% !
0.
!
∈
$
6
=
6 - − .6
6
=
6 ,6
1 /−
/ /
1 5
1/
.
. - . #
∈
/
&
-
+
+
∈
"
+
- .
+
7
. =
&%3+
= # -
+
+
+ −
+
. =
-
;
+
+
"
+
!=
∈
+
+ . +
9
+
+/
+ +
+
+
+
+
+
- .
+
4
+
+/
−
- . =
+
!
% !
"
.
-7 3&
+
+/
'
+
7%
! !%%
∈
!%% 3
A
%!
% !
"
# !=
6
= 22,
B 6 - − B.6
%&' .
.
&
% %
0
& &
= -B . =
-
.
−
+/
!0
B & !
=
+
- .
+
. =
4
&
&
@
.
.
+ −- + .
+/
%% 3 # ! 3
/ !0 > %
!0
&
:
0 ! ' ! < !&
+
+/
. =
.=
%3
8 % !"
+
/
"
-
∈
# %
98 % %
!"
!% 3 + ; & "
!%%
& % +
.
+
- . #
+
; &
&
-
. =
--
#
- +.
- .=
& "
%&+
2
/
+
+
& ! +
,
%% 3
=
;
∈
$
-$
?
&
∈
.
!
!#
!%% 3 # 3!
!%%
0!
!&
B CC
!%%
!%%
08&
0! A
!% 3 +
&
'!
0!
!' !
%
%
- .= -
"
-
+
& %
−
- .=
+
"
!%
!
!% ! #
]( ) =
=
!% ! !&@
(
−/
!% 3 + !
B
=
#
?
?
5
,
% &!
−
2
( )
1/
- .
!(
)
% %
" % %
# !% <
!%
- + .1/ .
! G& &@
! G& &@
,
#
! G
!
'!
!!
- + .
- .
?
# &
?
!!
)
5
( ) ( ) (−
2
= ,# # / # # 1 /#
! '!
- . >
+
= 2,,2
?
!
!!
5
2
'!
/
&
5
5
&0
!! !0
!% 3 +
=
*.+
−
&
0 "
= - − .1/ - 0
%
?
%
=
G
%
F
E#
-
+
> [ 1 - 1 /. −
H
,
# D
! $
+
≤ 1/ D
. =
# /# 2#
&
= ,# #/# # - − . 1 / #
!
,≤
" @'!
.# 0 &%
−
# $! ' !
G
>;
2
&0
−/
1/
)
2
&
= −?
−?
& &@
1/
D!
# !&@
% &!
0&
I
!% ! !&@
!% 3 +
&
!KL@
&@
=
!
( )
−
N
(−
J− +
J
−
1
( )
4 (− )
" @&
! !% 3
!!
;
- ! 7 $.#
!!
)
−
!
!!
=,
0.
=,
−/
J
−
G 0 &
M /K4 ,
7 $ &@
1/∉ #
=
( )=,
&%3+
.
/ =
(
+
)
=
=,
4
=,
0.
)J
=
( )=/
(− )
− 1
!0
& "
.
(
!0
,=, =
(
−
)
()
−
⋅
()
=
- .
-− .
=,
-− . - .
4
=,
&
G
&
JCC
0&
!%
%
!% 3 +
(
/
−
2
)
!
!!
(
!%
N
&
+
!&
)
2 J
−
/
(
=
J
=
-− . - . -
/
-− . - .
/ +
.
()
J
−
/
& %
+
/
!0
=,
!
(
!!
2
−
)
-
(
J−
# ,≤
2
/
)
2 J
−
0&
−
2
)
=
J
+
( )J
=,
/
−
2
.
≤J
.
=,
4
=,
0
!' %
/ + # ,≤
> B
!G
≤ J# , ≤
/ +
> N#
& N
≤
%
!
+ ,≤
0 &
≤B
= ,
= ,
/ +
= ,
=
= ,#
/ +
= /#2
= /
= ,# # /
/ +
= B # ?# 5
= 2
= , # # /# 2
/ +
= 5# I #N#J
= B
= ,# # /# 2# B
/ +
= N # J# ,#
E# ! %
() ()
J
2
( !
2
/
%
& "
() ()
J
B
$
&# !%
N
!& !%
%
B
,
&
N
2
( ) + ( ) = 2IN
J
2
J
B
= 2#
# /#
=/
= B#
=,
,C
=
=
!% !
-− . -
−
−/
. ?/
−/
//
5
+/
=,
−
=
!% 3 +
-− . -
−
− .
. -? / . -
⋅ - / / ⋅ 5. ⋅ / − / ⋅ 5 /
=,
4 /? ⋅
−
25
B
-− . -
; 0
"
=,
()
. /?
− −
/B
=,
4 /? ⋅ J -/? − /B.
C
−
=
=
−
= //?
()
8
!% 3 +
"
=,
&
()
−
=
( )=
" '! & +
,
8
% # +, 4
=,
( )(− )
+
=
( )(− )
8
4
=,
( )(− ) #
!% !
#
= '
8%%
N#
'
/
&
!
!
- + . =
=,
&%3+;
.
;
()
&
- + . =
=,
.
;
)
∀ ∈
" +
()
−
!&
+
−
%% 3
4
(
# ∈
+
=
=,
=
()
−,
,
,
−
∈
'!
( )
()
+
=
+
% +
−
& +
- + .
+
+
=
=,
&
( )
+
+ −
" +
- + .
#
+
= - + . - + . =
7 3&
- + .
+
%&' #
=
- .
- + .
0&
+
−
+
=,
+
4
=
4
=
- + .
−
- .
=,
4
+
=,
( )
+
−
=,
( )
+ −
( )
+ −
−
−
+
( )
+
=,
+
( )
( )
F
=
+ −
+
( )
+ −
+
( )
,
+ −
+
4
4
( )
( )
+
[( )
+
=
+
,
+
−
( )
+
+
=
( )]
+ −
+ −
+
( )
+
4
=,
( )
+
+ −
9
+
,
=
∴- + . =
=,
()
−
∀ ∈
L- .
( )= ( )
,
,
+
+
( )
=
( )= ( )
+
+
=
+