Question

Calcule a solução das equações:
B) x+x/3+x/9+x/27+...=60
C)x+3x+...+729x=5465

Answer 1

b)

$S_{\infty} = \frac{a_{1}}{1 -q}$

60 -x = (x/3)/(1 -1/3)
60 -x = x/3 . 3/2
60 -x = x/2
120 = 3x
120/3 = x
40 = x

c) $A_{n} = a_{1} . Q^{(n -1)}$

729x = x . 3ⁿ ⁻¹
3⁶ = 3ⁿ ⁻¹

7 = n

$S_{n} = \frac{a_{1} . (q^n -1) }{q -1}$

5465 = x . (3⁷ -1)/2
10930 = x . 2186
10930/2186 = x
5 = x