let-consider-for-all-n-1-the-real-t-n-t-t-1-t-n-1-Find-L-n-0-t-1-t-n-1-dt-

Tinku Tara June 3, 2023 Integration 0 Comments

Question Number 67466 by ~ À ® @ 237 ~ last updated on 27/Aug/19

let consider for all n≥1 the real (t)_n =t(t+1).....(t+n−1) Find L_n = ∫_0 ^∞ (((t)_1 )/((t)_(n+1) )) dt

$$ \\ $$$$ \\ $$$${let}\:{consider}\:\:\:{for}\:{all}\:{n}\geqslant\mathrm{1}\:{the}\:{real}\:\left({t}\right)_{{n}} \:={t}\left({t}+\mathrm{1}\right)…..\left({t}+{n}−\mathrm{1}\right) \\ $$$${Find}\:\:\:{L}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({t}\right)_{\mathrm{1}} }{\left({t}\right)_{{n}+\mathrm{1}} }\:{dt} \\ $$

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let-consider-for-all-n-1-the-real-t-n-t-t-1-t-n-1-Find-L-n-0-t-1-t-n-1-dt-

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