Answer: This is a classic problem in mathematics known as the arithmetic series or the Gauss sum.
To find out how many days the person can donate with a total of Rs. 210, we need to sum the sequence of donations until we reach the total amount of Rs. 210. The sequence of donations is:
1 + 2 + 3 + 4 + 5 + ... + n
The sum of the sequence can be expressed as:
n(n+1)/2
So we need to solve the equation:
n(n+1)/2 = 210
n(n+1) = 420
n^2 + n - 420 = 0
We can solve this quadratic equation using the quadratic formula:
n = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 1, and c = -420.
n = (-1 ± sqrt(1^2 - 4(1)(-420))) / 2(1)
n = (-1 ± sqrt(1 + 1680)) / 2
n = (-1 ± sqrt(1681)) / 2
n = (-1 ± 41) / 2
Since we are looking for a positive integer value of n, we can discard the negative solution:
n = (41 - 1) / 2
n = 40 / 2
n = 20
Therefore, the person can donate for a maximum of 20 days with a total donation of Rs. 210, starting with Rs. 1 on the first day and increasing by Rs. 1 each day.
Explanation: