# 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.