Calcular el valor de :2 + 4 + 8 + 16 + 32 + ?

Sucesiones :

formula general :

<img src="https://tex.z-dn.net/?f=%20a_%7Bn%7D%20" /> = <img src="https://tex.z-dn.net/?f=%20a_%7B1%7D%20" /> + ( n - 1 )r

<img src="https://tex.z-dn.net/?f=%20a_%7Bn%7D%20" /> = último número

<img src="https://tex.z-dn.net/?f=%20a_%7B1%7D%20" /> = primero número

n = cantidad de número

r = razón

formula progresión geometrica :

<img src="https://tex.z-dn.net/?f=%20a_%7Bn%7D%20" /> = <img src="https://tex.z-dn.net/?f=%20a_%7B1%7D%20" />.

Rⁿ⁻¹

suma de progresión geometrica :

<img src="https://tex.z-dn.net/?f=%20s_%7Bn%7D%20" /> = a_{1} .

(rⁿ - 1) / r - 1

1.

- 2 + 4 + 8 + 16 + 32 + .

(25 sumandos)

a_{n} : x

a_{1} : 2

n : 25

r : 2

a_{n} = 2.

2²⁴

a_{n} = 2²⁵

<img src="https://tex.z-dn.net/?f=%20s_%7Bn%7D%20" /> = 2(2²⁵ - 1) / 2 - 1

2²⁶ - 2 / 1

67108862

2.

- 4 + 8 + 16 + 32 + .

(20 sumandos)

<img src="https://tex.z-dn.net/?f=%20a_%7Bn%7D%20" /> = 4.

2¹⁹

<img src="https://tex.z-dn.net/?f=%20a_%7Bn%7D%20" /> = 2²¹

[img = 10] = 4(2²⁰ - 1) / 2 - 1

[img = 11] = 2²² / 1

[img = 12] = 4194304.