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JEE Plances Class Answered

ques 28
Asked by chandanbr6004 | 19 Nov, 2017, 17:32: PM
answered-by-expert Expert Answer
begin mathsize 16px style sum from straight i equals 1 to straight n of straight a subscript straight i straight b subscript straight i plus sum from straight i equals 1 to straight n of open parentheses straight a subscript straight i minus straight a close parentheses squared
equals sum from straight i equals 1 to straight n of straight a subscript straight i open parentheses 1 minus straight a subscript straight i close parentheses plus sum from straight i equals 1 to straight n of open parentheses straight a subscript straight i minus straight a close parentheses squared..... open curly brackets straight b subscript straight i equals 1 minus straight a subscript straight i close curly brackets
equals sum from straight i equals 1 to straight n of straight a subscript straight i minus sum from straight i equals 1 to straight n of straight a squared subscript straight i plus sum from straight i equals 1 to straight n of straight a squared subscript straight i minus 2 straight a sum from straight i equals 1 to straight n of straight a subscript straight i plus straight a squared sum from straight i equals 1 to straight n of 1
equals sum from straight i equals 1 to straight n of straight a subscript straight i minus 2 straight a sum from straight i equals 1 to straight n of straight a subscript straight i plus straight a squared sum from straight i equals 1 to straight n of 1
equals na minus 2 straight a cross times na plus straight a squared straight n
equals na open parentheses 1 minus straight a close parentheses..... left parenthesis 1 right parenthesis
now
nb equals sum from straight i equals 1 to straight n of straight b subscript straight i
nb equals sum from straight i equals 1 to straight n of open parentheses 1 minus straight a subscript straight i close parentheses
nb equals straight n minus na
straight b equals 1 minus straight a....... sub space in space left parenthesis 1 right parenthesis
ans space equals space nab


end style
Answered by Arun | 05 Dec, 2017, 16:16: PM
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