Maths · Evaluation of definite integrals
If then are in
If \( I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x, \) then \( \frac{1}{I_{2}+I_{4}}, \frac{1}{I_{3}+I_{5}}, \frac{1}{I_{4}+I_{6}}, \dots \) are in
- A. A.P
- B. G.P.
- C. н.P
- D. none
Step-by-step solution
Using reduction formula: I_n = 1/(n-1) - I_{n-2}, so I_n + I_{n-2} = 1/(n-1). Thus 1/(I_2+I_4)=3, 1/(I_3+I_5)=4, 1/(I_4+I_6)=5, ... which form an arithmetic progression with common difference 1.