Can someone please explain how the n is factored out of the 6n and ends up with the 7n. I must learn how to factor this and not just accept the answer.
I am having to make sure my question is understood. I do not think my message will line up properly. There is an example in my text that adds the sums of the area as part of the solution of calculating the definite integral of a function.. When I get to the part of adding the sums of the aresa:
= 3/n [(7+7+….7) + (6/n + 12/n +…6n/n) ]
= 3/n [ 7n + 6/n * (1 + 2+ ….n)]
= 3/n [ 7n + 6/n * n(n+1)/2
= 3/n [7n + 3 (n+1)]
= 3/n [7n + 3n + 3]
= 3/n [ 10n +3 ] = 30 + 9/n