Please help me for getting the displacement due to changing load , the equation is attached herewith

Please help me for getting the displacement due to changing load , the equation is attached herewith

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It is not obvious to me that the outer summation is necessarily convergent such that you could numerically truncate the infinite summation ?
Actually it is a general equation , I need rather for degree and order up to 50
You have an infinite summation in the equation. Is there reason to expect that the summation will converge?

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