If $$y = x + {x^2} + {x^3} + ...$$ up to infinite terms where x < 1, then which one of the following is correct?

The value of $${1 \over {{{\log }_3}e}} + {1 \over {{{\log }_3}{e^2}}} + {1 \over {{{\log }_3}{e^4}}} + ......$$ up to infinite terms is

If $$1.3 + {2.3^2} + {3.3^3} + ... + n{.3^n} = {{(2n - 1){3^a} + b} \over 4}$$, then a and b are respectively.

If $${S_n} = nP + {{n(n - 1)Q} \over 2}$$, where, S_n denotes the sum of the first n terms of an AP, then the common difference is