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let-f-n-x-n-0-e-nx-calculate-1-e-f-n-x-dx-




Question Number 30435 by abdo imad last updated on 22/Feb/18
let  f_n (x)=  Σ_(n=0) ^∞  e^(−nx)   calculate  ∫_1 ^e  f_n (x)dx.
$${let}\:\:{f}_{{n}} \left({x}\right)=\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{e}^{−{nx}} \:\:{calculate}\:\:\int_{\mathrm{1}} ^{{e}} \:{f}_{{n}} \left({x}\right){dx}. \\ $$

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