AP EAMCET2011MathematicsDefinite Integration
If I_n= ₀^ / 4 ^n d for n=1,2,3, , then I_ n-1 +I_ n+1 is equal to
Options
- A0
- B1
- C1 n
- D1 n+1
Correct answer
C. 1 n
Step-by-step solution
Given, I_n= ₀^ / 4 ^n d aligned & I_ n-1 +I_ n+1 = ₀^ / 4 ^ n-1 d & + ₀^ / 4 ^ n+1 d & = ₀^ / 4 ^ n-1 (1+ ^2 ) d & = ₀^ / 4 ^2 ^ n-1 d aligned Put = ^2 d =d aligned I_ n-1 +I_ n+1 & = ₀^1 ^ n-1 d & = [ ^n n ]₀^1= 1 n aligned