functions - Getting terms and only evaluate specific parts

I want to expand the expression but I do not want it to evaluate.

Sum[(HoldForm[1/(2 # - 1) - 1/(2 # + 1)] &)[i], {i, 1, 6}]

However if you evaluate this you get: (Fraction-Fraction)+...+(Fraction-Fraction). What i want is to have this fraction evaluated without having to evaluate the subtraction inside the parenthesis or the addition outside the parenthesis. Could someone show me a simple way to do this?

Answer

HoldForm[# - #2] & @@@ Table[{1/(2 i - 1), 1/(2 i + 1)}, {i, 1, 6}] // Total

Comments

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