Find the sum of the following convergent series. (a) ∑ j=0
[infinity]
​
( 3
i
​
) j
(b) ∑ k=0
[infinity]
​
(1+i) k
3
​
(c) ∑ j=0
[infinity]
​
(−1) j
( 3
2
​
) j
(d) ∑ k=14
[infinity]
​
( 2i
1
​
) k
(e) ∑ j=0
[infinity]
​
( 3
1
​
) 2j
(f) ∑ j=0
[infinity]
​
[ j+2
1
​
− j+1
1
​
]