Question

1 Write the series 3 + 6x +9x2 +12x + ... with 45 terms in sigma notation.​

Answer 1

Explanation:

It looks like every time the coefficient increases by 3 while the exponent increases by 1.

`\\45\\\sum 3(n+1)x^(n)\\n = 0`

Notice it starts at zero so 3 is multiplied by (x+1) to make it start from 0

The exponent is simply n, because at the start is it zero
`x^0=1`, then 1, then 2, so on.

The upper limit is 45 because 45 - 0 = 45 terms