Which of the following two terms is larger: \( \sum_{i=1}^n i^2 \) or \( \sum_{i=1}^{n^2} i \).
Difficulty level
This exercise is mostly suitable for students
Both of these terms can be independently solved and compared.
We can observe that: Sum 1 to n i^2 = n.(n+1).(2n+1)/6 , while sum 1 to n*n i = n^2.(n^2 +1)/2 .
Thus, the second term is significantly larger for larger values of n.Back to the list of exercises
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