Question

Va rog ajutati-ma . Ex 25 si daca vreti si 26. Am nevoie urgent.

Answer 1

Răspuns:

Explicație pas cu pas:

25

aₙ = (-1)¹+(-1)²+(-1)³+.......+(-1)ⁿ =

= -1 + 1 -1 +1 +.....(-1)ⁿ = (-1)ⁿ  =

= -1  daca n numar impar

= 1 daca n = numar par

bₙ = (-1)¹·(-1)²·(-1)³·.....·(-1)ⁿ = (-1)¹⁺²⁺³⁺⁻⁻⁻⁻⁺ⁿ

1+2+3+....+n = (n+1)·n:2 = (n²+n)/2   ; n≥1

n = 1 => bₙ = -1  

n = 2 => bₙ = -1

n = 3 => bₙ = 1

n = 4  => bₙ = 1

n = 5 => bₙ = -1

n = 6 => bₙ = -1

n = 7 => bₙ = 1

n = 4k  ; n = 4k-1  => bₙ = 1

n = 4k-2 ; n = 4k-3  => bₙ = -1

aₙ+bₙ = ?

n = 4k  =>  aₙ+bₙ = 1+1 = 2

n = 4k-1  => aₙ+bₙ= -1+1 = 0

n = 4k-2 => aₙ+bₙ = 1-1 = 0

n = 4k-3 => aₙ+bₙ = -1-1 = -2

aₙ·bₙ = ?

n = 4k => aₙ·bₙ =1·1 = 1

n = 4k-1  => aₙ·bₙ =1·(-1) = -1

n = 4k-2 =>  aₙ·bₙ =1·(-1) = -1

n = 4k-3 => aₙ·bₙ = (-1)·(-1) = 1

26

E(n) = (-1)ⁿ·2n ; n∈N

I E(1)+E(2)+....+E(100) I = ?

E(1) = (-1)¹·2·1 = -2

E(2) = (-1)²·2·2 = 4

E(3) = (-1)³·2·3 = -6

E(4) = (-1)⁴·2·4 = 8

--------------------------------------

E(100) = (-1)¹⁰⁰·2·100 = 200

I E(1)+E(2)+....+E(100) I = I -2+4-6+8-10+12-........+200 I

= I 2+2+2+.....+2I (50 de perechi de cate 2 numere)=

=I 100 I = 100

I E(1)+E(2)+....+E(100) I = 100