Sum: x + 3x ^ 2 + 5x ^ 3 +... + (2n-1) x ^ n

Sum: x + 3x ^ 2 + 5x ^ 3 +... + (2n-1) x ^ n

Analysis: when x = 0, x + 3x ^ 2 + 5x ^ 3 +... + (2n-1) x ^ n = 0; when x = 1, x + 3x ^ 2 + 5x ^ 3 +... + (2n-1) x ^ n = 1 + 3 + 5 +... + (2n-1) = n (1 + 2n-1) / 2 = n & # 178; when x ≠ 0 and X ≠ 1, let s = x + 3x ^ 2 + 5x ^ 3 +... + (2n-1) x ^ n, then: XS = x & # 178; + 3x & # 179; + 5x ^ 4 + 7x ^ 5 +... + 178