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Question Number 152722 by SANOGO last updated on 31/Aug/21

Answered by Olaf_Thorendsen last updated on 31/Aug/21

• I = ∫_0 ^1 (e^(−(1/x)) /x^2 ) dx Let u = (1/x) : I = ∫_1 ^∞ e^(−u) du = [−e^(−u) ]_1 ^∞ = (1/e) (1) • I = ∫_0 ^1 (e^(−(1/x)) /x^2 ) dx I = lim_(n→∞) (1/n)Σ_(k=0) ^n (e^(−(1/(k/n))) /(k^2 /n^2 )) I = lim_(n→∞) nΣ_(k=0) ^n (e^(−(n/k)) /k^2 ) (2) (1) and (2) : lim_(n→∞) nΣ_(k=0) ^n (e^(−(n/k)) /k^2 ) = (1/e)

∙I=∫01e−1xx2dxLetu=1x:I=∫1∞e−udu=[−e−u]1∞=1e(1)∙I=∫01e−1xx2dxI=limn→∞1n∑nk=0e−1knk2n2I=limn→∞n∑nk=0e−nkk2(2)(1)and(2):limn→∞n∑nk=0e−nkk2=1e

Commented by SANOGO last updated on 31/Aug/21

merci bien mon prof

mercibienmonprof

Commented by Olaf_Thorendsen last updated on 31/Aug/21

Je ne suis pas prof.

Jenesuispasprof.

Commented by SANOGO last updated on 31/Aug/21

ok merci bien c′est gentil

okmercibienc′estgentil

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