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CBSE Class 10 Answered

Answer the following
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Asked by tultuldutta58 | 08 Jan, 2018, 03:34: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight S subscript straight n equals straight n over 2 open square brackets 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d close square brackets space space space space space.... left parenthesis straight i right parenthesis
straight S subscript 2 straight n end subscript equals fraction numerator 2 straight n over denominator 2 end fraction open square brackets 2 straight a plus left parenthesis 2 straight n minus 1 right parenthesis straight d close square brackets space space space space space.... left parenthesis ii right parenthesis
straight S subscript 3 straight n end subscript equals fraction numerator 3 straight n over denominator 2 end fraction open square brackets 2 straight a plus left parenthesis 3 straight n minus 1 right parenthesis straight d close square brackets space space space space space.... left parenthesis iii right parenthesis
Now comma
straight S subscript 2 straight n end subscript minus straight S subscript straight n equals fraction numerator 2 straight n over denominator 2 end fraction open square brackets 2 straight a plus left parenthesis 2 straight n minus 1 right parenthesis straight d close square brackets minus straight n over 2 open square brackets 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d close square brackets
space space space space space space space space space space space space space space space equals straight n over 2 open square brackets 2 left curly bracket 2 straight a plus left parenthesis 2 straight n minus 1 right parenthesis straight d minus left curly bracket 2 straight a plus left parenthesis straight n minus 1 right parenthesis straight d right curly bracket close square brackets
space space space space space space space space space space space space space space space equals straight n over 2 open square brackets 2 straight a plus left parenthesis 3 straight n minus 1 right parenthesis straight d close square brackets
fraction numerator straight S subscript 3 straight n end subscript over denominator straight S subscript 2 straight n end subscript minus straight S subscript straight n end fraction equals fraction numerator fraction numerator 3 straight n over denominator 2 end fraction open square brackets 2 straight a plus left parenthesis 3 straight n minus 1 right parenthesis straight d close square brackets over denominator straight n over 2 open square brackets 2 straight a plus left parenthesis 3 straight n minus 1 right parenthesis straight d close square brackets end fraction
rightwards double arrow fraction numerator straight S subscript 3 straight n end subscript over denominator straight S subscript 2 straight n end subscript minus straight S subscript straight n end fraction equals 3 over 1
end style
Answered by Rashmi Khot | 08 Jan, 2018, 08:47: AM
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