Question #5: solve the system of equations below using substitution.

I need someone to find a mistake in my soliution or maybe to solf it much more easily... I have got a sum  

1+

1

4⋅

2

4

+

1

7⋅

2

7

+

1

10⋅

2

10

+⋯

1+14⋅24+17⋅27+110⋅210+⋯

and need to evaluate it. So here's my soliution:  

S(x)=1+

x

4

4⋅

2

4

+

x

7

7⋅

2

7

+

x

10

10⋅

2

10

+⋯=1+

∑

n=1

∞

x

3n+1

(3n+1)⋅

2

3n+1

=1+

S

1

(x)

21

step-by-step explanation: