The question is attached.

Asked by sudhanshubhushanroy | 8th Dec, 2017, 06:39: AM

Expert Answer:

begin mathsize 16px style Let space straight d space be space the space common space difference space of space the space given space straight A. straight P.
Then comma space straight a subscript 2 minus straight a subscript 1 equals straight a subscript 3 minus straight a subscript 2 equals....... equals straight a subscript straight n minus straight a subscript straight n minus 1 end subscript equals straight d
Now comma
fraction numerator 1 over denominator square root of straight a subscript 1 end root plus square root of straight a subscript 2 end root end fraction plus fraction numerator 1 over denominator square root of straight a subscript 2 end root plus square root of straight a subscript 3 end root end fraction plus fraction numerator 1 over denominator square root of straight a subscript 3 end root plus square root of straight a subscript 4 end root end fraction plus....... plus fraction numerator 1 over denominator square root of straight a subscript straight n minus 1 end subscript end root plus square root of straight a subscript straight n end root end fraction
equals fraction numerator square root of straight a subscript 2 end root minus square root of straight a subscript 1 end root over denominator open parentheses square root of straight a subscript 2 end root plus square root of straight a subscript 1 end root close parentheses open parentheses square root of straight a subscript 2 end root minus square root of straight a subscript 1 end root close parentheses end fraction plus fraction numerator square root of straight a subscript 3 end root minus square root of straight a subscript 2 end root over denominator open parentheses square root of straight a subscript 3 end root plus square root of straight a subscript 2 end root close parentheses open parentheses square root of straight a subscript 3 end root minus square root of straight a subscript 2 end root close parentheses end fraction plus......
plus fraction numerator square root of straight a subscript straight n end root minus square root of straight a subscript straight n minus 1 end subscript end root over denominator open parentheses square root of straight a subscript straight n end root plus square root of straight a subscript straight n minus 1 end subscript end root close parentheses open parentheses square root of straight a subscript straight n end root minus square root of straight a subscript straight n minus 1 end subscript end root close parentheses end fraction
equals fraction numerator square root of straight a subscript 2 end root minus square root of straight a subscript 1 end root over denominator straight a subscript 2 minus straight a subscript 1 end fraction plus fraction numerator square root of straight a subscript 3 end root minus square root of straight a subscript 2 end root over denominator straight a subscript 3 minus straight a subscript 2 end fraction plus..... plus fraction numerator square root of straight a subscript straight n end root minus square root of straight a subscript straight n minus 1 end subscript end root over denominator straight a subscript straight n minus straight a subscript straight n minus 1 end subscript end fraction
equals fraction numerator square root of straight a subscript 2 end root minus square root of straight a subscript 1 end root over denominator straight d end fraction plus fraction numerator square root of straight a subscript 3 end root minus square root of straight a subscript 2 end root over denominator straight d end fraction plus..... plus fraction numerator square root of straight a subscript straight n end root minus square root of straight a subscript straight n minus 1 end subscript end root over denominator straight d end fraction
equals 1 over straight d open parentheses square root of straight a subscript straight n end root minus square root of straight a subscript 1 end root close parentheses
equals fraction numerator open parentheses square root of straight a subscript straight n end root minus square root of straight a subscript 1 end root close parentheses open parentheses square root of straight a subscript straight n end root plus square root of straight a subscript 1 end root close parentheses over denominator straight d open parentheses square root of straight a subscript straight n end root plus square root of straight a subscript 1 end root close parentheses end fraction
equals fraction numerator straight a subscript straight n minus straight a subscript 1 over denominator straight d open parentheses square root of straight a subscript straight n end root plus square root of straight a subscript 1 end root close parentheses end fraction
equals fraction numerator straight a subscript 1 plus left parenthesis straight n minus 1 right parenthesis straight d minus straight a subscript 1 over denominator straight d open parentheses square root of straight a subscript straight n end root plus square root of straight a subscript 1 end root close parentheses end fraction
equals fraction numerator straight n minus 1 over denominator square root of straight a subscript 1 end root plus square root of straight a subscript straight n end root end fraction end style

Answered by Rashmi Khot | 8th Dec, 2017, 10:21: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.