Question

Find the sum of the series 1.2 + 2.3x + 3.4x^2 + .....

Answer 1

the answer is 4.5x^4
it is correct

Answer 2

Answer:

Step-by-step explanation:

1rst order differences; 4,6,8,10,....

2nd order differences;2,2,2,2,....

Scale of the series=(1-x)^(n+1). (Where n is the second order difference hence n=2)

(1-x)^3=1-x^3-3x+3x^2

S=2+6x+12x^2+20x^3+30x^4+....

-3xS=-6x-18x^2-36x^3-60x^4-....

3x^2S=6x^2+18x^3+36x^4+....

-x^3S=-2x^3-6x^4-....

S-3xS+3x^2S-x^3S=2. (Taking S common)

S=2/(1-x)^3 (Answer)