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Exercise:
Valuta lim_n to inftyfracx_nprod_i^n- x_i sapo che x_nx_n-^- x_.

Solution:
footnotehttps://math.stackexchange.com/questions//evaluatthvaluof-lim-n-to-infty-fracx-n-prod-i-n--x-i-whe Sappiamo che: x_nx_n-^-Rightarrow x_n^x_n-^-x_n-^+Rightarrow x_n^-x_n-^x_n-^- Dunque x_n^-x_n-^x_n-^- Ripeto il processo con x_n- abbiamo che x_n^-x_n-^x_n-^-x_n-^x_n-^x_n-^-ldotsx_^-prod_i^n-x_i^ E quindi insero x_ otteniamo prod_i^n-x_ifracsqrtx_n^-sqrt Concludo e sapo che x_nto infty perché x_n è crescente otteniamo che lim_nto infty fracx_nprod_i^n-x_ilim_nto inftyfracx_nsqrtsqrtx_n^-lim_nto inftyfracsqrtsqrt-fracx_n^sqrt
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Exercise:
Valuta lim_n to inftyfracx_nprod_i^n- x_i sapo che x_nx_n-^- x_.

Solution:
footnotehttps://math.stackexchange.com/questions//evaluatthvaluof-lim-n-to-infty-fracx-n-prod-i-n--x-i-whe Sappiamo che: x_nx_n-^-Rightarrow x_n^x_n-^-x_n-^+Rightarrow x_n^-x_n-^x_n-^- Dunque x_n^-x_n-^x_n-^- Ripeto il processo con x_n- abbiamo che x_n^-x_n-^x_n-^-x_n-^x_n-^x_n-^-ldotsx_^-prod_i^n-x_i^ E quindi insero x_ otteniamo prod_i^n-x_ifracsqrtx_n^-sqrt Concludo e sapo che x_nto infty perché x_n è crescente otteniamo che lim_nto infty fracx_nprod_i^n-x_ilim_nto inftyfracx_nsqrtsqrtx_n^-lim_nto inftyfracsqrtsqrt-fracx_n^sqrt
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Extra, Successioni e serie
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ITA (Italiano)
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Calculative / Quantity
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