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受欢迎的代数 >

vn+1=vn*(n+1)(n+3)(n+2)^2

解答

v n + 1 = v n \cdot (n + 1) (n + 3) (n + 2)^{2}

解答

v = \frac{1}{n ( n ^{4} + 8 n ^{3} + 23 n ^{2} + 28 n + 11 )}; n \neq = 0, n \neq = - 0.72798 \dots, n \neq = - 3.27201 \dots

求解步骤

v n + 1 = v n (n + 1) (n + 3) (n + 2)^{2}

展开

v n (n + 1) (n + 3) (n + 2)^{2} : n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v

v n + 1 = n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v

将

1

到右边

v n = n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v - 1

两边减去

n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v

v n - (n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v) = n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v - 1 - (n^{5} v + 8 n^{4} v + 23 n^{3} v + 28 n^{2} v + 12 n v)

化简

- n^{5} v - 8 n^{4} v - 23 n^{3} v - 28 n^{2} v - 11 n v = - 1

分解

- n^{5} v - 8 n^{4} v - 23 n^{3} v - 28 n^{2} v - 11 n v : - n v (n^{4} + 8 n^{3} + 23 n^{2} + 28 n + 11)

- n v (n^{4} + 8 n^{3} + 23 n^{2} + 28 n + 11) = - 1

两边除以

- n (n^{4} + 8 n^{3} + 23 n^{2} + 28 n + 11); n \neq = 0, n \neq = - 0.72798 \dots, n \neq = - 3.27201 \dots

v = \frac{1}{n ( n ^{4} + 8 n ^{3} + 23 n ^{2} + 28 n + 11 )}; n \neq = 0, n \neq = - 0.72798 \dots, n \neq = - 3.27201 \dots

作图

流行的例子

solvefor a,(a)x-|x|=0

so l v e f or a, (a) x - ∣ x ∣ = 0

t (t) = t^{2} + 5 t + 6

solvefor x,13x+14y-9=0

so l v e f or x, 13 x + 14 y - 9 = 0

solvefor c, 114982/3*c*m^3= 4/3*22/7*r^3

so l v e f or c, \frac{114982}{3} \cdot c \cdot m^{3} = \frac{4}{3} \cdot \frac{22}{7} \cdot r^{3}

solvefor x,(f)+4f=x-2

so l v e f or x, (f) + 4 f = x - 2