Calculate the Sum of Geometric Series: 1 + 5² + 5³ + 5⁴ + ... + 5²⁰³⁵

This is a geometric series with first term 1 and common ratio 5. The sum of the first n terms of a geometric series with first term 'a' and common ratio 'r' is given by:

S_n = a(1 - r^n) / (1 - r)

So in this case, we have:

a = 1 r = 5 n = 2035

S_2035 = 1(1 - 5^2035) / (1 - 5) S_2035 = (1 - 5^2035) / (-4)

This is a very large number, approximately equal to:

-1.249 × 10^340

So the sum of the series is approximately -1.249 × 10^340.