# A calculus problem by Vraj Mehta

Calculus Level 5

If The Tangent at $$P_1$$ on the curve $$3y=x^3+1$$ meets the curve again at $$P_2$$.

The tangent at $$P_2$$ meets the curve at $$P_3$$ and so on.

Then Let the sum of the $$\textbf{ordinates}$$ for $$P_1,P_2,P_3,\cdots P_{60}$$ be $$\beta$$.

$$\text{Then Find}$$

$$\beta +\dfrac{2^{183}-8}{27}$$

$$\textbf{Note :}$$

$$P_1$$ Is the Point other Than The Point Of Inflection.

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