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Naina Razdan Grade:
        

Evaluate the limit


lim n tends to infinity


tanA + 1/2 tan A/2 + 1/4 tan A/4 + ... 1/2n tan A/2n

6 years ago

Answers : (1)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
										

Dear Eshita,


Ans:- Let F(A)=tan A+ 1/2 tanB+.............


So, F(A)dA= (tanA+1/2tanA/2+1/4tanA/4+.......................)dA


      ∫F(A)dA =∫(tanA+1/2tanA/2+.................)dA


                 =(ln secA+ln secA/2 +....................+ln secA/2^π) +C


                    =ln(secA secA/2 secA/4...............secA/2^n) +C


                        =ln(2^n/(cosA cosA/2 cosA/4..............)+C


                        =ln (2^n sinA/2^n/sin2A) +C


Again differentiating both sides we get,


F(A)=(1/2^n) cot(A/2^n)  - 2cot2A


 


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Regards,


Askiitians Experts


SOUMYAJIT IIT_KHARAGPUR

6 years ago
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