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Question no. 14

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Asked by Payal 21st February 2018, 4:57 PM
Answered by Expert
Answer:
begin mathsize 16px style According space to space the space question space 1 comma 2 comma 3 comma.... straight p space and space
common space ratios space 1 half comma 1 third comma 1 fourth.... comma fraction numerator 1 over denominator straight p plus 1 end fraction
Sum space of space infinite space GP space equals fraction numerator straight a over denominator 1 minus straight r end fraction
Find space straight S subscript 1 comma straight S subscript 2...... straight S subscript straight p
you space get
straight S subscript 1 space equals 2 comma space straight S subscript 2 space equals 3 comma....... comma straight S subscript straight p equals straight p plus 1
From space this space we space can space observe space that space sums space are space in space AP space with space straight a equals 2 space and space straight d equals 1
straight p over 2 open square brackets 2 cross times 2 plus open parentheses straight p minus 1 close parentheses cross times 1 close square brackets equals fraction numerator straight p left parenthesis straight p plus 3 right parenthesis over denominator 2 end fraction end style
Answered by Expert 21st February 2018, 5:23 PM
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