Question

Halla "S" S= 6/3+10/9+14/27+18/81+...

Answer 1

Respuesta:

S = 4

Explicación paso a paso:

S = 6 / 3 + 10 / 9 + 14 / 27 + 18 / 81 + .......

Multiplicar:

3S = 3(6 / 3 + 10 / 9 + 14 / 27 + 18 / 81 + ......)

3S = 6 + 10 / 3 + 14 / 9 + 18 / 27 + ......

Restar:

3S = 6 + 10 / 3 + 14 / 9 + 18 / 27 + ......

S =          6 / 3 + 10 / 9 + 14 / 27 + 18 / 81 + .......

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2S = 6 + 4 / 3 + 4 / 9 + 4 / 27 + .........

2S = 6 + 4(1 / 3 + 1 / 9 + 1 / 27 + .........)

2S = 6 + 4M

Luego:  

M = 1 / 3 + 1 / 9 + 1 / 27 + .........

Multiplicar:

3M = 3(1 / 3 + 1 / 9 + 1 / 27 + .........)

3M = 1 + 1 / 3 + 1 / 9 + .........

3M = 1 + M

3M - M = 1

2M = 1

M = 1 / 2

Reemplazar:

2S = 6 + 4M

2S = 6 + 4(1 / 2)

2S = 6 + 2

2S = 8

S = 4