Rmo Inmo Stimulators 2014

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𝒖𝒏 = 𝒖𝒏 ∈ (

𝟏

,

(𝟏+(βˆ’πŸ)𝒏)+𝟏

{𝒖𝒏 }

πŸ“π’+πŸ” πŸ‘πŸ—

𝟏𝟎𝟎 𝟏𝟎𝟎

[πŸπŸ–]

)

[πŸ‘πŸŽπŸŽ] π’Ž

π’Ž&𝒏

𝒏

{ 𝟏 < 𝒂 < 𝒃 + 𝒄 < 𝒂 + 𝟏, 𝒃 < 𝒄

πŸπŸ“ πŸπŸ” πŸπŸ• πŸπŸ– πŸπŸ— πŸ‘πŸŽ πŸ—

,

,

,

,

,

𝟏𝟎 𝟏𝟏 𝟏𝟐 πŸπŸ‘ πŸπŸ’

}

𝒂 < 𝒃.

π₯𝐨𝐠 πŸ‘ πŸπŸŽπŸ– , π₯𝐨𝐠 πŸ“ πŸ‘πŸ•πŸ“ ? 𝟏 √𝟏

+

𝟏 √𝟐

+

𝟏 βˆšπŸ‘

+ ⋯….+

|π’”π’Šπ’π’ŽπœΆ| ≀ π’Ž|π’”π’Šπ’πœΆ| (πŸπ’)! (𝒏!)𝟐

>

πŸ’π’

𝟏 βˆšπ’

> βˆšπ’

𝒏 β‰₯ 𝟐.

π’Ž ∈ β„•& 𝜢 ∈ ℝ 𝒏 > 𝟏.

𝒏+𝟏

[πŸπŸπŸ–πŸ•] πŸπŸŽπŸ’ 𝟎, 𝟏, 𝟐, πŸ‘ & πŸ“ [πŸ‘πŸ] [πŸ“πŸ•πŸ”] [πŸ’πŸ“. πŸπŸŽπŸ“ ] {𝟏, 𝟐, πŸ‘, πŸ’, πŸ“, πŸ”, πŸ•, πŸ–} [πŸπŸ‘πŸ•πŸ] {𝟏, 𝟐, πŸ‘} [πŸ”πŸ•πŸ]

𝟐

[πŸπŸ—πŸ’πŸ–πŸ’πŸŽ] 𝟐. πŸπŸŽπŸ– {𝟎, 𝟏, 𝟐}

πŸ‘ 𝟎

[πŸ’πŸ‘πŸ•πŸ‘] [πŸ“πŸ•πŸ”]

πŸπŸ– [πŸπŸ”πŸπŸ—πŸ•πŸ] 𝟐. πŸπŸŽπŸ– 𝟏 &𝟐

[πŸ•πŸ”πŸ”]

[πŸπŸ•πŸ—πŸ“πŸ“πŸŽ] 𝒏𝒏+𝟏 > (𝒏 + 𝟏)𝒏 𝒏 β‰₯ πŸ‘, 𝒏 ∈ β„•

π’‚πŸ , π’‚πŸ , π’‚πŸ‘ , … ….

π’ƒπŸ , π’ƒπŸ , π’ƒπŸ‘ , … …. π’„πŸ , π’„πŸ , π’„πŸ‘ , … …. 𝒏

𝒄𝒂𝒏 = 𝒃𝒏 + 𝟏

𝒄𝒏+𝟏 𝒄𝒏 βˆ’ (𝒏 + 𝟏)𝒄𝒏+𝟏 βˆ’ 𝒏𝒄𝒏

𝒂𝒏+𝟏 > 𝒃𝒏

[πŸπŸŽπŸπŸ‘πŸ ]; [𝟐𝟎𝟏𝟏𝟐 βˆ’ 𝟐]; [πŸπŸŽπŸ—πŸ—]

π’‚πŸπŸŽπŸπŸ‘ , π’ƒπŸπŸŽπŸπŸ , π’„πŸπŸŽπŸπŸŽ

π’™πŸ + 𝒂𝒙 + 𝒃 = 𝟎

π’™πŸ + 𝒃𝒙 + 𝒄 = 𝟎

π’™πŸ + 𝒄𝒙 + 𝒂 = 𝟎 π’‚πŸ + π’ƒπŸ + π’„πŸ (π’Ž + 𝒏)πŸ’ = π’ŽπŸ π’πŸ + π’ŽπŸ + π’πŸ + πŸ”π’Žπ’

π’Ž, 𝒏

πŸπ’™ + πŸπŸŽπŸŽπŸ— = πŸ‘π’š πŸ“π’›

(πŸπ’)! < [𝒏(𝒏 + 𝟏)]𝒏

𝒏 ∠π‘ͺ

π’™π’š + π’š 𝒙 = π’›π’š

π‘ͺπ‘«πŸ < 𝑨π‘ͺ. 𝑩π‘ͺ

βˆ†

π’™π’š + 𝟐𝟎𝟏𝟐 = π’šπ’›+𝟏

πŸπ’™πŸ‘ + 𝟏 = πŸ‘π’›π’™ πŸπ’šπŸ‘ + 𝟏 = πŸ‘π’™π’š πŸπ’›πŸ‘ + 𝟏 = πŸ‘π’šπ’›

𝟏

𝟏

𝟏

𝟐

𝟐

𝟐

[(𝟏, 𝟏, 𝟏), (βˆ’ , βˆ’ , βˆ’ )]

±⊑±⊑±⊑±⊑±⊑±⊑ ⊑ ±

⊑ +

βˆ’

π’‡βˆΆ ℝ β†’ ℝ 𝒇 𝒇 𝒇 𝒇 𝒇(𝒏)

𝒇 𝒇

ℝ ℝ

𝒇 𝒇

𝒇

𝒇

ℝ 𝒇 𝟏𝟎𝟎𝟎𝟎

𝟏𝟎𝟎𝟏𝟎𝟎𝟎 [π₯𝐨𝐠 𝑿 𝒀]

𝟏𝟎𝟎𝟎𝟎𝟎

𝟏𝟎𝟎𝟎𝟏𝟎𝟎𝟎𝟎 𝟐 𝒙 βˆ’ πŸ‘π’™ + πŸ“ = 𝟎

𝜢, 𝜷

𝒏 πœΆπ’ + πœ·π’ βˆ’ πŸ‘π’

πŸ“. [𝟎. πŸ“πŸŽπŸπŸ“] π’Œ 𝒆 𝒙 βˆ’ 𝒙𝒆 = π’Œ

{𝟎, 𝟏, 𝟐, πŸ‘} 𝒙

𝒏 𝑺𝒏 𝝅 πŸŽβ‰€π’™β‰€

π’”π’Šπ’πŸ’π’™ β‰₯ π’”π’Šπ’π’™

π₯𝐒𝐦 𝑺𝒏

𝟐

π’β†’βˆž

π‘ͺ𝟏 : (𝒙 βˆ’ 𝒂)𝟐 + π’šπŸ = π’‚πŸ

𝒂, 𝒃 π‘ͺ𝟐 : π’™πŸ +

π’šπŸ π’ƒπŸ

=𝟏

𝒃 = 𝟏/βˆšπŸ‘

(𝒑, 𝒒) 𝒙 β‰₯ 𝒑

𝒂

[𝒂] [βˆšπ’]

𝒏 ≀ 𝟏𝟎𝟎𝟎𝟎

𝒏 π‘ͺ: π’š = π’™πŸ‘ βˆ’ πŸ‘π’™πŸ + πŸπ’™

𝑳 ∢ π’š = 𝒂𝒙

𝒂 𝑺(𝒂) 𝒂 𝒏 π’‚πŸ =

𝟏 𝒏(𝒏+𝟏)

𝒂 𝑺(𝒂) π’‚π’Œ = βˆ’

𝟏 π’Œ+𝒏+𝟏

{π’‚π’Œ } 𝒏 + βˆ‘π’Œπ’Š=𝟏 π’‚π’Š , (π’Œ = 𝟏, 𝟐, πŸ‘ … … ) π’Œ

π’‚πŸ 𝒂𝒏𝒅 π’‚πŸ‘ . π’‚π’Œ 𝒃𝒏 =

βˆ‘π’π’Œ=𝟏 βˆšπ’‚π’Œ

π₯𝐒𝐦 𝒃𝒏 = π₯𝐧 𝟐

𝟐

π’β†’βˆž 𝟐

𝒙 + π’š + π’›πŸ = πŸ”

𝒙, π’š, 𝒛 ∈ ℝ , 𝒙 + π’š + 𝒛 = πŸ’

𝒛. [𝟐]

𝒑(𝒙) = πŸπ’™πŸ—πŸ– + πŸ‘π’™πŸ—πŸ• + πŸπ’™πŸ—πŸ” + πŸ‘π’™πŸ—πŸ“ + β‹― . . +πŸπ’™ + πŸ‘ = 𝟎 [𝟐] π’Ž π’™πŸ βˆ’ π’Žπ’™ + 𝟏 < 𝟎

πŸβ‰€π’™β‰€πŸ [πŸ‘]

𝒑(𝒙) [𝟎]

𝒑(𝟏) = 𝟐, 𝒑(πŸ‘) = 𝟏 π’™πŸπŸŽπŸŽπŸ• βˆ’ 𝟏

(π’™πŸ + 𝟏)(π’™πŸ + 𝒙 + 𝟏) [πŸ‘]

𝒑(𝒙) 𝒑(𝒂) = 𝒑(𝒃) = 𝒑(𝒄) = βˆ’πŸ. 𝒂, 𝒃, 𝒄 > 𝟎 π’‚πŸ = 𝒃𝒄 𝒂 + 𝒃 + 𝒄 = 𝒂𝒃𝒄 π’™πŸ + π’™πŸ + π’™πŸ‘ = 𝟏 𝒙 𝟏 π’™πŸ + π’™πŸ π’™πŸ‘ + π’™πŸ‘ π’™πŸ = 𝟏

𝒂, 𝒃, 𝒄

[𝟎] [πŸ‘] |π’™πŸ | + |π’™πŸ | + |π’™πŸ‘ | π’™πŸ π’™πŸ π’™πŸ‘ = 𝟏 [πŸ‘] 𝒑(𝒙) = π’™πŸπŸŽπŸŽ βˆ’ πŸπ’™πŸ—πŸ— + πŸ‘π’™πŸ—πŸ– βˆ’ β‹― … . βˆ’πŸπŸŽπŸŽπ’™ + 𝟏𝟎𝟏 = 𝟎 [𝟎] [𝟎] π’™πŸ’ βˆ’ π’šπŸ’ = πŸ‘πŸ–πŸ•πŸ—πŸπŸŽπŸ–. 𝒇(𝒙) = π’‚π’™πŸ + πŸπ’ƒπ’™ + 𝒄, 𝒂, , 𝒃, 𝒄 ∈ ℝ 𝒇(𝒙) 𝒙 [𝟎] 𝒙 𝒂 βˆ’π’‚ 𝜢, 𝜷, 𝜸 π’™πŸ‘ βˆ’ πŸ‘π’™πŸ + 𝒂𝒙 βˆ’ 𝒂 = 𝟎 [πŸ—] (𝜢 βˆ’ πŸ‘)πŸ‘ + (𝜷 βˆ’ πŸ‘)πŸ‘ + (𝜸 βˆ’ πŸ‘)πŸ‘ = 𝟎 𝒂 𝒃 πŸπŸŽπ’‚ + 𝒃 = πŸ“ 𝒑(𝒙) = π’™πŸ + 𝒂𝒙 + 𝒃. 𝒏 [πŸπŸπŸ“] 𝒑(𝟏𝟎)𝒑(𝟏𝟏) = 𝒑(𝒏) π’™πŸ + π’™πŸ + π’™πŸ‘ = πŸπŸ’ 𝟏 ≀ π’™πŸ ≀ πŸ“ [πŸ‘πŸ“] 𝟏𝟐 ≀ π’™πŸ ≀ πŸπŸ– βˆ’πŸ ≀ π’™πŸ‘ ≀ 𝟏𝟐 𝑢 ≑ (𝟎, 𝟎) 𝑨 ≑ (πŸ—, πŸ”)

𝑷 ≑ (πŸ‘, πŸ‘)

𝑸 ≑ (πŸ”, πŸ’)

𝒑(𝒙).

π’‚πŸ .

[πŸπŸŽπŸπŸ“]

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