Show that the sum of n A.Ms between two given numbers is n times the single A.M between them.

Asked by Olivia Adhikary | 19th Aug, 2014, 11:03: AM

Expert Answer:

l e t space n u m b e r s space b e space A space a n d space B I n s e t i n g space n space A M s space b e t w e e n space a b o v e space n u m b e r s B equals A plus left parenthesis n plus 1 right parenthesis d space w h e r e space d space i s space t h e space c o m m o n space d i f f e r e n c e d equals fraction numerator B minus A over denominator n plus 1 end fraction  S u m space o f space n space A M apostrophe s space i s space g i v e n space b y n over 2 open square brackets 2 open parentheses A plus d close parentheses plus open parentheses n minus 1 close parentheses d close square brackets equals n over 2 open square brackets 2 A plus n d plus d close square brackets equals n A plus fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction d b u t space d equals fraction numerator B minus A over denominator n plus 1 end fraction  rightwards double arrow n A plus fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction d equals n A plus fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction open square brackets fraction numerator B minus A over denominator n plus 1 end fraction close square brackets equals n A plus n over 2 open parentheses B minus A close parentheses equals n open parentheses A plus fraction numerator B minus A over denominator 2 end fraction close parentheses equals n open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses equals S u m space o f space n space A M apostrophe s  G i v e n space s t a t e m e n t space i s space w r o n g. space P l e a s e space v e r i f y space y o u r space q u e s t i o n

Answered by Dharma Teja | 19th Aug, 2014, 04:12: PM

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