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Sir pls solve the following.
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Asked by rsudipto | 28 Dec, 2018, 07:53: PM
answered-by-expert Expert Answer
Let r be the common ratio of the given G.P.
 
Sum of 100 even-number-place terms  = begin mathsize 12px style sum from n equals 1 to 100 of a subscript 2 n end subscript space equals space a subscript 2 space plus space a subscript 4 space plus space a subscript 6 space plus............... a subscript 200 space equals space a subscript 2 fraction numerator r to the power of 200 minus 1 over denominator r squared minus 1 end fraction space equals space alpha space............. left parenthesis 1 right parenthesis end style
Sum of 100 odd-number-place terms  = begin mathsize 12px style sum from n equals 1 to 100 of a subscript 2 n minus 1 end subscript space equals space a subscript 1 space plus space a subscript 3 space plus space a subscript 5 space plus............... a subscript 199 space equals space a subscript 1 fraction numerator r to the power of 200 minus 1 over denominator r squared minus 1 end fraction space equals space beta space............. left parenthesis 2 right parenthesis end style
( It is to be noted here, in a given geometric progression series that has common ratio r, if we consider even-number-term series and
odd-number-term series separately, their common ratio is r2)
 
if we divide eqn.(1) by eqn.(2), we get = begin mathsize 12px style a subscript 2 over a subscript 1 space equals space alpha over beta space equals space r end style
Hence common ratio of series α/β
Answered by Thiyagarajan K | 29 Dec, 2018, 08:26: PM

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