Final answer:
To find the sum of the geometric sequence 1+5+…+390625+1953125, use the formula for the sum of a geometric series. The sum is approximately 488281.
Step-by-step explanation:
To find the sum of the geometric sequence 1+5+…+390625+1953125, we can use the formula for the sum of a geometric series. The formula is S = a * (1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 1, the common ratio (r) is 5, and the number of terms (n) can be found by setting 5^n = 1953125 and solving for n. By taking the logarithm of both sides, we find that n ≈ 9.
Plugging in the values, we have S = 1 * (1 - 5^9) / (1 - 5) ≈ 1 * (1 - 1953125) / -4 ≈ -1953124 / -4 = 488281.