vanshika9086
vanshika9086 vanshika9086
  • 21-10-2016
  • Mathematics
contestada

Find the value of 2^1/2. . 4^1/8 . 8^1/16. . 16^1/32 ..........infinity

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HeavenlyHelper
HeavenlyHelper HeavenlyHelper
  • 21-10-2016
tn=n/2^(n+1) tn+1=(n+1)/2n+2=n/2n+2+1/2n+2 tn+1=tn/2+1/2n+2 t2=t1/2+1/2^3 t3=t2/2+1/2^4 . . . --------------------- adding Sn-t1=Sn/2 +(1/2^3+1/2^4+.........) Sn/2=t1+(1/2^3+1/2^4....)

Sn/2=1/4+(1/2^3)(1/(1-1/2)) =1/4+1/4 Sn=1

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