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SEMANA 3:

NUMERACIN I

1. Calcule a si:

( )

( )( )7 .

9

pa n 2c 1 aa

3 = +

Adems ( )( )

n

p

c5p7 4c3

2

=

A) 2 B) 3 C) 4D) 5 E) 6

RESOLUCIN

( ) ( ) ( ) ( ) ( )n p 9 7c p

5p7 4c3 a n 2c 1 aa2 3

= = +

n 7> p 4> n 9< c 3< C! pa" p 3#6=

n ! $ p 6= c 2=

%ue&':

( ) ( )9 7a2$ 5aa=

$1a 2 9 $ 245 7a a+ + = + +$1a 26 245 $a+ = +73.a 219 a 3= =

RPTA.: B

2. (Cun's *al'"es puede 'ma" +

en( )

n

n

+,-125

++ =

A) 4 B) 5 C) 6D) 7 E) $

RESOLUCIN

( )

( )

= =n

n

+ 1,-125

$++

Desc'mp'niend'

+ 1 ++n + $

= = + + /1 n)+

1$

=

1 1n 1 $

n 1 $= = + =

+ n 7=

0e"' + n 7< =+ 123456= puede 'ma" 6 *al'"es

RPTA.: C

3. i:

( ) ( ) ( ) ( )( )

( )7n 5

n n 1 n 2 n 3 n 4 acd+

+ + + + =

alle: ( )a c d+ + +

A) 1, B) 12 C) 13D) 11 E) 14

RESOLUCIN

/7)/n 5)n/n 1)/n 2)/n 3)/n 4) acd++ + + + =

( )n 5 7+ < n 1=

( )/6) 712345 acd=

1 2 3 4 5

6 6 4$ 3,6 1$6,

1 $ 51 31, 1$65

a!5

( ) ( )771$65 53,3 acd = = !3

C!, D!3

a c d ! 11

RPTA.: B

4. alle ( )m n p+ + - si ( ) ( )n n 111, -$1 +

/n 1)1mp s'n nme"'s c'nsecui*'s.

A) 15 B) 14 C) 13

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D) 12 E) 11

RESOLUCIN

( ) ( ) ( )n 1n n 111, $1 1mp +

0'" da': ( ) ( )n n 111, 1 $1 ++ = ( )2n n 1 $ n 1 1+ + = + +

( ) ( )2n 7n $ , n $ n 1 , = + =n 8 $ n!$n 1

( ) ( ) ( )7$ 911, $1 1mp

72 73 74

74 7 4 1, 7

3 1

( ) ( )7 71mp 134 m 3p 4 n $= = = =

m n p 15+ + =

RPTA.: A

5. aiend' ue : ( ) ( )n 9a7 a'c =adems ( ) ( )n 5 .6d6 mm= alle el*al'" de /m d).

A) 2 B) 4 C) 3D) 6 E) $

RESOLUCIN

( ) ( )n 9a7 a'c

+ =

7 n 9 n $< < =

ami;n p'" da':

( ) ( )$ 56d6 mm=

( )2 2

56 $ d $ 6 m .5 + + = ( )5mb+

39, $d+ 26= m ( )5

( )5195 4d 13.m+ =

, 15

( ) ( )5 5d , m 15 3,= = =

m ! 3 ! ,3dm

=++RPTA.: C

6. Calcule el *al'" de n si m esm

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( ) ( )( )

( ) ( ) ( )( )9 9

a 1 c 2 c 1 3 3< 5+ + = +

?&ualand':

@ c ! 5

@ 1 3 2+ = =@ a 1a 1= =@c 2 3< + = +5 2 3< + = + 7 3< = + < ! 2 ! 1

0ide: a c < 11+ + + + =

RPTA.: C

$. En la si&uiene e 4

A) 27 B)3 C)85D) 83 E)5

RESOLUCINmna4

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RESOLUCIN

( )( )( ) ( ) = n$131216F Base ( )1n+

( ) ( ) ( ) ( ) ( )

( ) ( )

( )( ) ( ) ( ) ( )

( )( ) ( )

( )( ) ( )

( ) ( )

( ) ( )

( )

nn

n n

n n nn

nn

nn

n n

n n

n

16 12 13 $ n 1 1111 1576 11

5 12 11 143 11

5 5 47

7 13 44

7 7 36

6$ 33

66 3

2

+ =

/n 1)F ...32 + =

de las 2 limas ci"as ! 5

RPTA.: C

12. i se cumple:

( )

( )

A), B) 2 C) 3

D)5 E) 6

RESOLUCIN

( ) ( )n 7a< ccn .../?)= C 2> a>

7n