Question Number 101231 by 175 last updated on 01/Jul/20

Commented byDwaipayan Shikari last updated on 01/Jul/20

(1/n).(π/6)lim_(n→∞) ((2^(1/n) −1)/(1/n)) Σ_(r=0) ^n (2^(r/n) cos(2^(r/n) (π/6)))  (π/6) log2 ∫_0 ^1 2^x cos(2^x (π/6))dx  ∫_0 ^1 cos(2^x (π/6))2^x (π/6)log2dx   ∫_(π/6) ^(π/3) cost dt =[sint]_(π/6) ^(π/3) =(((√3)−1)/2)  {suppose 2^x (π/6)=t}

Answered by smridha last updated on 01/Jul/20

(𝛑/6)lim_(n→∞) ((2^(1/n) −1)/(1/n)).[lim_(n→∞) (1/n).Σ_(r=0) ^n 2^(r/n) .cos(2^(r/n) .(𝛑/6))]  =(𝛑/6).ln(2).∫_(0 ) ^1 2^x .cos(2^x .(𝛑/6))dx  =(𝛑/6).ln2.(6/(𝛑.ln(2)))∫_0 ^1 d[sin(2^x .(𝛑/6))]  =1.[sin(2^x .(𝛑/6))]_0 ^1 =[sin(𝛑/3)−sin(𝛑/6)]      =((√3)/2)−(1/2)=(((√3)−1)/2).

Commented by175 last updated on 01/Jul/20

thanx

Commented bysmridha last updated on 01/Jul/20

welcome...but careful there is a group 😄😄😄😄