Word Count : 432

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To solve the recurrence relation numerically using the method of telescoping sums, we analyze: \[ a_{n+1} = a_n + n \cdot 2^n, \quad (n \geq 0), \quad a_0 = 1. \] ### Step 1: Expanding the First Few Terms We expand the recurrence relation for the first few values: \[ a_1 = a_0 + 0 \cdot 2^0 = 1 + 0 = 1. \] \[ a_2 = a_1 + 1 \cdot 2^1 _________ ________ _______ _________ ____ ______.
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