Final answer:
The student's total savings after 365 days of saving an additional cent each day will be ¢66,795, calculated using the formula for the sum of an arithmetic series.
Step-by-step explanation:
If a student saves ¢1 on the first day, ¢2 on the second day, ¢3 on the third day, and so on, his total savings in 365 days can be calculated using the formula for the sum of an arithmetic series. To find the sum, we use the formula: S = n/2 × (a1 + an), where S is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term. In this case, the student saves for 365 days, so n is 365, a1 is ¢1, and an is ¢365.
Using the formula, we calculate the total savings as:
S = 365/2 × (1 + 365) = 365/2 × 366 = 183 × 365 = ¢66,795
Therefore, the student's total savings after 365 days would be ¢66,795.