To my knowledge, the answer should be there is no difference since I found the sum, however the answer is something else,
could someone please explain

In the first series, the summation applies to the whole (2n+3) inside the parentheses, so the 3 gets summed up 5 times.
But in the second one, the summation only applies to the 2n , so the 3 is only added after the summation is finished.
The difference between five 3s the first time and one 3 the second time is your 12 .

Answered by AL2006 | 2024-06-10

The difference between them is 12 because : the sum of first series is : 2 * ( 1 + 2 + 3 + 4 + 5 ) + 15; the sum of the second series is : 2 * ( 1 + 2 + 3 + 4 + 5 ) + 3.

Answered by crisforp | 2024-06-10

The difference in summation results often arises from how terms are explicitly defined within the summation. When constants are summed directly versus added after summation leads to differing totals. Understanding the nuances of summation notation will help clarify these discrepancies.
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Answered by AL2006 | 2024-12-26