If \(b_n= ∫_0^{\frac{π}{2}} \frac{cos^2nx}{sinx }dx, n∈N,\) Then
- b3 – b2, b4 – b3, b5 – b4 are in an A.P. with a common difference –2
- \(\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}, \text{ are in an A.P. with common difference 2}\)
- b3 – b2, b4 – b3, b5 – b4 are in a G.P.
- \(\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}, \text{ are in an A.P. with common difference -2}\)
The Correct Option is A
Solution and Explanation
The correct option is(D): \(\frac{1}{b_3-b_2},\frac{1}{b_4-b_3},\frac{1}{b_5-b_4}, \text{ are in an A.P. with common difference -2}\)
are in A. P. with common difference –2.
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Concepts Used:
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There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
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Partial Differential Equations:
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Linear Differential Equations:
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Homogeneous Differential Equations:
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Read More: Differential Equations