anonymous
  • anonymous
the value of 2^(1/4).4^(1/8).8^(1/16).16(1/32)........................ is?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
2^(1/4+2/8+3/16+.....)
anonymous
  • anonymous
find the sum of AGP series....1/4+2/8+3/16+4/32
anonymous
  • anonymous
2^(13/16)

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anonymous
  • anonymous
this is not an AP, the 1st n 2nd term are the same isnt it?
anonymous
  • anonymous
yes it is AGP....
anonymous
  • anonymous
1/2^2 +(1+1)/2^3+(1+2)/2^4+(1+3)/2^5
anonymous
  • anonymous
AGP is airthmatic geomatric series
anonymous
  • anonymous
got it?????
anonymous
  • anonymous
tn=n/2^(n+1)
anonymous
  • anonymous
from tn you have to find Sn. here the series is small so you can add but otherwise you have to use series method.........
anonymous
  • anonymous
whats the series method??
anonymous
  • anonymous
check the page http://www.ilovemaths.com/3sequence.asp
anonymous
  • anonymous
this is an infinite series i guess we gotta use Sn= a/1-r need to break the question itno that form
anonymous
  • anonymous
no this form will not be applicable........
anonymous
  • anonymous
tn=n/2^(n+1) \[t _{n+1}=(n+1)/2^{n+2}=n/2^{n+2}+1/2^{n+2}\] \[t _{n+1}=t _{n}/2+1/2^{n+2}\] 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....)
anonymous
  • anonymous
Sn/2=1/4+(1/2^3)(1/(1-1/2)) =1/4+1/4 Sn=1
anonymous
  • anonymous
hence 2^1=2
anonymous
  • anonymous
Got it?????
anonymous
  • anonymous
i think u have understood

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