Tuesday, 10 March 2015

sequences and series - To prove sum of A.P is greater than G.P

Consider an Arithmetic Progression(A.P) with the first term $a$, the commom difference $d$ and a Geometric Progression(G.P) with first term again as $a$ but common ratio $r$ such that $a,d,r>0$ and both these progressions have same number of terms and their last terms are also equal.



Show that the sum of all the terms of A.P is greater than the sum of all the terms of the G.P.



My Attempt:




The terms between first and last terms are the $(n-2)$ Arithmetic Means(A.M's) or the Geometric Means(G.M's). Can it be proved that each of the A.M's is greater than the corresponding G.M's.

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