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Q.
- Identify type of series: Identify the type of series.The series , , ..., is an arithmetic series because the difference between consecutive terms is constant.
- Find first and last term: Find the first term and the last term of the series.The first term is and the last term is .
- Calculate number of terms: Calculate the number of terms in the series.Since the series is consecutive integers from to , we can find the number of terms by subtracting the first year from the last year and adding .
- Use formula for sum: Use the formula for the sum of an arithmetic series.The sum of the first terms of an arithmetic series is given by:
- Substitute values into formula: Substitute the values into the formula to find the sum.
- Verify the result: Verify the result.To check for a math error, we can quickly verify by adding the first and last term to see if it matches the sum we used in the formula:Since this matches the sum we used in the formula, it seems we have not made a math error.
