I am trying to use the "Summation" command for the exponent and for the corresponding subscript of the coefficient, but it fails. See the example below:

```
Sum[ai*x^i, {i, 1, 5}] = a x + 2 a x^2 + 3 a x^3 + 4 a x^4 + 5 a x^5

```

I want:

```
a1 x + a2 x^2 + a3 x^3 + a4 x^4 + a5 x^5

```

In a little complex form, I want the following expression to write "Summation":

```
(a0 + a1*x^1 + a2*x^2 + a3*x^3 + a4*x^4 + a5*x^5)/(b0 + b1*x^1 + 
 b2*x^2 + b3*x^3 + b4*x^4 + b5*x^5)

```

Likewise, how to make "Table" instead of "Summation" with or without the coefficients:
e.g.:

```
Table[x^i, {i, 1, 5}]/Table[x^j, {j, 0, 5}]

```

I want an output of the form:

```
{x^1, x^2, x^3, x^4, x^5}/{x^0, x^1, x^2, x^3, x^4, x^5}

```

Can someone have a look at this, please? Thanks.