A) \[1.2+2.3+3.4+4.5+.........\]
B) \[\frac{G}{{{A}^{2}}}\]
C) \[\frac{{{A}^{2}}}{G}\]
D) \[\frac{A}{{{G}^{2}}}\]
Correct Answer: A
Solution :
Let the positive number \[{{a}_{1}}\] and \[{{a}_{2}}\] \[{{a}_{1}},\,A,\,{{a}_{2}}\]????A.P. then \[A=\frac{{{a}_{1}}+{{a}_{2}}}{2}\] \[{{G}^{2}}=AH\] ????.G.P. \[G=\sqrt{{{a}_{1}}{{a}_{2}}}\] \[\frac{1}{{{a}_{1}}},\,\frac{1}{H},\,\frac{1}{{{a}_{2}}}\]??..H.P. \[\frac{2}{H}=\frac{1}{{{a}_{1}}}+\frac{1}{{{a}_{2}}}\]; \[H=\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}\]; \[H=\frac{{{G}^{2}}}{A}\]
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