Find the limit of the sequence given by 𝑎𝑛=6+10+14+...+(4𝑛−2)𝑛2a n = n 2 6+10+14+...+(4n−2) , (where 𝑛∈𝑁∖{0}n∈N∖{0}).
Question
Solution 1
The given sequence is an arithmetic series with a common difference of 4, divided by n^2.
The sum of an arithmetic series can be found using the formula: S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the last term.
In this case, a_1 = 6 and a_n = 4n - 2.
So, S_n = n/2 * (6 + Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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