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Pour les articles homonymes, voir Hulk (homonymie). Hulk.mw-parser-output .entete.persofiction{background-image:url("//upload.wikimedia.org/wikipedia/commons/3/37/Picto_infobox_masks.png")} Personnage de fiction apparaissant dans The Incredible Hulk . Statue représentant Hulk lors de la sortie du film Avengers (2012). Nom original Hulk Alias Robert Bruce Banner (véritable identité) (Hulk) : le Titan Vert, le Colosse de jade, le Roi Vert, la Balafre Verte, Holku, le Fils de Sakaar, le Vert, Œil de Rage, le Briseur de Mondes, Harkanon, Haarg, Plus-Sauvage, Deux-Esprits, Captain Universe, le Professeur, Guerre, le Maestro, Joe Fixit/Mr Fixit, l’Annihilateur, Méchano (aussi été possédé par Nul) [ 1 ] (Bruce Banner) : Robert Baker, Bruce Bancroft, David Banner, David Bannon, Bruce Barnes, Bruce Baxter, Mr Bergen, Bruce Bixby, David Bixby, Bob Danner, Bruce Davidson, Bruce Franklin, Bruce Green, Bruce Jones, Ross Oppenheimer, Bruce Roberts, Bruc...

0 $begingroup$ Let $(a_n)_{n∈N}$ be a sequence of positive numbers which tends to zero but such that $sum_{n=1}^infty a_n$ diverges. Let $(A_n)_{n∈N}$ be the sequence of partial sums $A_n=sum_{k=1}^n a_k$ ,and let $b_{n+1}=sqrt{A_{n+1}}−sqrt{A_{n}}$ . Show that $lim_{n→∞}frac{b_n}{a_n}= 0$ but that $sum b_n$ is still divergent. Question 1: I was able to answer the first part, since $$frac{b_{n+1}}{a_{n+1}} = frac{sqrt{A_{n+1}}−sqrt{A_{n}}}{a_{n+1}} = frac{A_{n+1}-A_n}{a_{n+1}(sqrt{A_{n+1}}+sqrt{A_{n}})} = frac{1}{sqrt{A_{n+1}}+sqrt{A_{n}}}$$ which converges to $0$ since $sqrt{A_n}$ tends to infinity. The second part, I have no idea about. Apparently $$sum b_k = sqrt{A_n}$$ Why is this true? Question 2: It is also said that In this sense there is no ‘smallest’ divergent series, and one c...