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# If $\;a_{1},a_{2},\;....\;a_{n}$ are in HP then $\;\large\frac{a_{1}}{a_{2}+a_{3}+\;..\;+a_{n}}\;,\large\frac{a_{2}}{a_{1}+a_{3}+...+a_{n}}\;,\large\frac{a_{3}}{a_{1}+a_{2}+a_{4}+\;...\;+a_{n}}\;,.....\;\large\frac{a_{n}}{a_{1}+a_{2}+....+a_{n-1}}\;$ are in

$(a)\;HP\qquad(b)\;GP\qquad(c)\;AP\qquad(d)\;None$

Explanation : Let $\;S=a_{1}+a_{2}+....+a_{n}$
$\frac{S}{a_{1}}-1\;,\frac{S}{a_{2}}-1\;....\;\frac{S}{a_{n}}-1$ are in AP
Given sequence which is the reciprocal of above is in HP.