Calculo IACC

Título del Control INDUCCION Y SUMATORIAS

Nombre Alumno ROSA MELBA CARCAMO MIRANDA

Nombre Asignatura CALCULO

Instituto IACC

26 DE MARZO DEL 2014

Desarrollo

1.- ∑_(k=10)^42▒(5K^(2 )-4K-1) = 42 [5(〖10)〗^(2 )-4(10)-1 ]

42 [5(100) -40-1 ]

42 [500 -40-1 ]

42 [459]

=19278

2.- Teorema numero 1

〖∑_(k=1)^n▒(k+1) (K+2)〗^ =1/4 n (n+1)(n+2)(n+3)

〖∑_(k=1)^1▒1(1+1) (1+2)〗^ = 1/4 1 (1+1)(1+2)(1+3)

1(2)(3) = 1/4 (1) (2)(3)(4)

6 = 24/4

= 6

Se comprueba que el teorema de inducción P(1) es V.

Teorema numero 2

〖∑_(k=1)^k▒k(k+1) (K+2)〗^ = 1/(4 ) k(k+1) (k+2) (k+3)k

K[k(k+1)(k+2)] (k(k+1) (k+2) (k+3)k)/4

K[k(k+1)(k+2) ( K^(4 )+ 6K^(3 ) 11K^2+6k)/4

[K^(2 )(K+1)(K+2)] (k(+ 6K^ +11k+6K^2+K^(3 ) )/4

K^(2 )(K^(2 )+2K+1K+2) K^(2 )(K^(2 )+3k+2)

K^(2 )(K^(2 )+3K+2)

(K(K+3)(K+1)(K+2))/4

(K^(2 )+3K(K+1)(K+2))/4

(K^(2 )+3K(K^(2 )+2K+K+2))/4

((K^(2 )+3K)( K^(2 )+3K+2))/4

K^(2 ) ( K^(2 )+3K+2)

Se comprueba que el teorema de inducción P(k) es V.

Teorema numero 3

(k+a)[((k+1)+1)((k+1)+2)] = 1/(4 )[(k+1) (k+1+1)((k+1)+2) (k+1)+3)]

(k+1)[ (k+1) (k+2) (k+3)] 1/(4 )[(k+1) (k+2)((k+3) (k+4)]

(K+1)^(2 ) [(k+2)(k+3) (k+4)/4 [(k+1) (k+2)(k+3)]

((k+4)(K+1))/4 [(k+2)(k+3)] (〖 K〗^(2 )+5k+4)/4

(K^(2 ) 4k+5k)/4

(〖 K〗^(2 )+5k+4)/4

3.- H=X(800)

〖 c〗_(6 )=6400

〖 c〗_9=51200

〖 c〗_2 L=Y

8X=8(6400)=51200

En 3 años aumento 8 veces =$134.400

Es decir que al cumpleaños Nº21 tendria $134.400.-

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