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2 1/4 4 1/8 8 1/16 16 1/32 32 1/64........up to infinity

21/441/881/16161/32321/64........up to infinity

Grade:11

2 Answers

Vandana Kumari
31 Points
6 years ago
S=21/422/823/1624/32....
S=21/4+2/8+3/16....
S=21/4(1+2/2+3/4+4/8....)
S=21/4(t)
t=1+2/2+3/4+4/8....   (infinite AGP with a=1,r=1/2,d=1)
t=a/(1-r) + dr/(1-r)2
t=2+2=4
S=2
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

S = 2^(1/4) * 2^(2/8) * 2^(3/16) * 2^(4/32)....
S = 2^(1/4 + 2/8 + 3/16....)
S = 2^1/4(1+2/2+3/4+4/8....)
S = 2^1/4(t)
t = 1 + 2/2 + ¾ + 4/8 .... (infinite AGP with a=1,r=1/2,d=1)
t = a/(1-r) + dr/(1-r)2
t = 2+2 = 4
S = 2

Thanks and Regards

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