let-give-u-n-k-1-n-a-k-2-with-a-k-sequence-of-reals-a-k-gt-0-and-v-n-k-1-n-a-k-k-prove-that-u-n-converges-v-n-converges-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 28977 by abdo imad last updated on 02/Feb/18

let give u_n =Σ_(k=1) ^n a_k ^2 with (a_k ) sequence of reals/a_(k>0) and v_n =Σ_(k=1) ^n (a_k /k) . prove that u_n converges⇒(v_n )converges

$${let}\:{give}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{a}_{{k}} ^{\mathrm{2}} \:\:\:\:\:{with}\:\left({a}_{{k}} \right)\:{sequence}\:{of}\:{reals}/{a}_{{k}>\mathrm{0}} \\ $$$${and}\:{v}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{a}_{{k}} }{{k}}\:.\:{prove}\:{that}\:{u}_{{n}} {converges}\Rightarrow\left({v}_{{n}} \right){converges} \\ $$

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let-give-u-n-k-1-n-a-k-2-with-a-k-sequence-of-reals-a-k-gt-0-and-v-n-k-1-n-a-k-k-prove-that-u-n-converges-v-n-converges-

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