If P n -2 n -7- n -32 then P 3 isA- 32-7-2-72B- 2 - 3-7-3-32C- 2 - 3-7 - 3-3-32D- 23-7-n-32

The correct option is B (2 × 3 + 7) lt; (3 + 3)2 P(n) : (2n + 7) lt; (n + 3)2 For n = 3, P(3) = (2 × 3 + 7) lt; (3 + 3)2 ...

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Algebraic Expressions

If P n :2 n +...

Question

If P(n) : (2n + 7) < (n + 3)² then P(3) is

(3² + 7) < (2 + 7)²

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(2 × 3 + 7) < (3 + 3)²

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(2 × 3 + 7 x 3) < (3 + 3)²

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(2³ + 7) < (n + 3)²

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Solution

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^{n}^{+}^{1} P_{5} :^{n} P_{6} =

2 : 7

n

=

{X_{n}},

X_{n} = \frac{90}{7 (^{n} P_{n})} - \frac{^{n + 4} P_{3}}{^{n + 2} P_{n + 2}}, n \in N

^{n} P_{4} :^{n} P_{5} = 1 : 2

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