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Find the sum of the first terms of the following series, to the nearest integer.Answer:
Full solution
Q. Find the sum of the first terms of the following series, to the nearest integer.Answer:
- Determine Type: Determine if the series is arithmetic or geometric.The series does not have a common difference or a common ratio between terms, so it is neither a standard arithmetic nor a geometric series. However, we can observe that each term seems to be increasing by a factor that itself increases by each time. This suggests that the series is neither arithmetic nor geometric, but we can still calculate the sum by finding a pattern or rule for the series.
- Find Pattern: Find the pattern or rule for the series.The first term is . To get the second term, we add (). To get the third term, we add to the second term (). It seems that with each step, we are adding an incrementally increasing integer starting from . Let's continue this pattern to find the next six terms.
- Calculate Next Terms: Calculate the next six terms using the pattern.th term: th term: th term: th term: th term: th term: Now we have all nine terms: .
- Sum All Terms: Sum all the terms to find the total sum of the first terms.Sum = Sum =
- Round Sum: Round the sum to the nearest integer if necessary.The sum is already an integer, so no rounding is necessary.
