(a) Sum the series y = 1+2x + 3x² + 4x³ + • .. , lx| < 1. (b) If f(x) = xe-z/^ over the interval 0 < r < oo, find the mean and most probable values of r. f(r) is the probability density of r. (c) Evaluate I = Jo s. (d) Find the eigenvalues and normalized eigenvectors of the matrix 1 2 4 2 3 0 5 0 3 Are the eigenvectors orthogonal? Comment on this.

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