Power Of 2

Algebra Level 5

\(If\quad \frac { { 2 }^{ \alpha }+{ 2 }^{ \beta }+{ 2 }^{ \gamma }+\quad .\quad .\quad .\quad +{ 2 }^{ n } }{ 5000 } =\quad 2014.\quad \\ and\quad { 2 }^{ \alpha },\quad { 2 }^{ \beta },\quad .\quad .\quad .\quad ,\quad { 2 }^{ n }\quad are\quad a\quad total\quad of\quad 'm'\quad terms,\quad \\ then\quad find\quad the\quad value\quad of\quad (\alpha +\beta +\gamma +\quad .\quad .\quad .\quad +n)(m).\quad \)

Details : \(\alpha ,\quad \beta ,\quad \gamma ,\quad .\quad .\quad .,\quad n\quad are\quad positive\quad integers.\)

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