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please answer the attached img. which asks the value of given expressioon [ this might be unclear in image:sigma 1 to infinity ;n]

please answer the attached img.
 which asks the value of given expressioon [  this might be
unclear in image:sigma 1 to infinity ;n]

Question Image
Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
here, all you gotta do is to write tanx= (1 – cosx)/sinx
and sin2y=2sinycosy
this above formulas will turn the summation into a telescopic sum, and you will get the sum of n terms as
Sn= 2/sin2theta – 1/[2^(n – 1)*sin{x/2^(n – 1)}]
now putting limit n tends to infinity, we get
Sinfinity=  2/sin2theta – 1/theta

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