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Macauley's duration formula, proof and dedution needed-Finance economics

I am searching for deduction step by step of Macauly's duartion formula, or its special form that looks like this:

D= {(1+Y)/Y - [1+Y+T(c-Y)]/[(c(1+Y)^T-1))+Y]}

where :

D-duration

Y-yield to maturity rate

c-coupon rate

T-elapsed time to yield to maturity

I need this formula explained step by step and how do we get to this final form. I am sincearely grateful to any1 who can help me, but please, dont reply me with links, because i already scoped entire web and didnt find exact deduction and proof of this formula. So, i summon all Math genius to explain this formula to me. Thank You in advance :)