Power series p₁(x) and p2(x) are given below. P₁(x) = 1 + 7x +49x² + 343x³ +2401x² + ... P2(x) = 1 + 5x + 25x² + 125x³ +625x² + ... Write the first 5 terms of p₁(x) + p2(x) below, simplifying any like terms. 2 ✓+12x 0 +74x² + 46823 3026x¹✓+... Write the series compactly using summation notation: 8 (77 +57) 27 X n=0 Find the functions to which each series converges to find an expression that represents the final series. 1 (Hint: What transformation was performed upon = 1 + x + x² + x³ + x² + to generate *** 1 <- x each series?)

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