Suppose i have

A:=Plus @@ Table[2 (Pi/n) (i + 4), {i, 0, n/2, 1}]
B:=Plus @@ Table[ x , {i, (Pi/n), (n/2 + 1) (Pi/n), (Pi/n)}]

i need to determine the argument of the table on B, such that A=B for every $n\in\{2k|k\in\mathbb N\}$ (even numbers).

My attempt: I'm thinking about this summation: $$\sum_{i=0}^{n/2}\frac{2\pi}{n}(i+4)=\sum_{i=1}^{n/2 +1}\frac{2\pi}{n}((i-1)+4)=\sum_{i=1}^{n/2 +1}\frac{2\pi}{n}(i+3)$$ So, i got x=2(i+3). But when i test n=20, the results were different. Please help me. Thanks in advance.

N.B. If there's something unclear about my question please tell me, i will edit it asap when i get the notification. Thanks.

a = Sum[2 (Pi/n) (i + 4), {i, 0, n/2, 1}];
b = Sum[x, {i, (Pi/n), (n/2 + 1) (Pi/n), (Pi/n)}];
FullSimplify[a == b, Assumptions -> n/2 ∈ PositiveIntegers]

16 + n) π == 2 n x


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