Question Number 104243 by  M±th+et+s last updated on 20/Jul/20

prove that  π=2×(2/(√2))×(2/(√(2+(√2))))×(2/(√(2+(√(2+(√2))))))×.....

Answered by OlafThorendsen last updated on 20/Jul/20

sinx = 2sin(x/2)cos(x/2)  sinx = 2^2 sin(x/4)cos(x/4)cos(x/2)  ...  sinx = 2^n sin(x/2^n )cos(x/2^n )cos(x/2^(n−1) )...  to be continued...

Answered by Dwaipayan Shikari last updated on 20/Jul/20

2.(2/(√2)).(2/(√(2+(√2)))).(2/(√(2+(√(2+(√2))))))......  lim_(n→∞)   S_n =2^n ((1/(√2)).(1/(√(2+(√2)))).(1/(√(2+(√(2+(√2))))))......n)  S_n =2^n cos(π/4).(1/(2cos(π/8)2)).(1/(cos(π/(16))2)).(1/(cos(π/(32)))).....n  S_n =2^n cos(π/4).(1/2^n )((1/(cos(0)........cos(π/8))))    S_n =cos(π/4).((1/(cos(π/8))).(1/(cos(π/(16)))).(1/(cos(π/(32))))....)continue