The least value of n. such that $(1 + 3 +3^{2}+.........+3^{n})$ exceeds 2000, is

option 3 is the right answer

Series 1 + 3 + 32 +...+ 3n
It is a geometric series whose
common ratio is 3.
a + ar + ar2 + ...... + arn–1
3n+1 – 1 > 4000
3n+1 > 4000 + 1 = 4001
For n = 7.
38 = 6561 > 4001