# If P(2n – 1, n) : P(2n + 1, n – 1) = 22 : 7 find n.

Given: P(2n – 1, n) : P(2n + 1, n – 1) = 22 : 7

To find: value of n

We know,

So, according to question:

P(2n – 1, n) : P(2n + 1, n – 1) = 22 : 7

7(n + 2)(n + 1) = 22×2 (2n + 1)

7(n2 + n + 2n + 2) = 88n + 44

7(n2 + 3n + 2) = 88n + 44

7n2 + 21n + 14 = 88n + 44

7n2 + 21n – 88n + 14 – 44 = 0

7n2 – 67n – 30 = 0

7n2 – 70n + 3n – 30 = 0

7n(n – 10) + 3(n – 10) = 0

(n – 10)(7n + 3) = 0

The value of n = 10

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