Math answers of smth

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Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation Math, education, statistics, answer, solutions, open sourse. Presentation

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$𝟏𝐧 + 𝟐𝐧 + 𝟑𝐧 + … + 𝐤𝐧 shakldagi yigʻindilarni hisoblash uchun formula yaratish 7-03-1 Kamoldinov Doniyor$

 REJA:
 Induksiya nima?
1n + 2n + 3n + … + kn shakldagi
misollar turlari.
 Misollarning ishlanish formulalari.
 Formulalar kelib chiqishi.

𝑰𝑵𝑫𝑼𝑲𝑺𝑰𝒀𝑨 𝒏𝒊𝒎𝒂?
Induksiya (matematikada) — muhim isbotlash usullaridan
biri; matematik induksiya aksiomasiga (prinsipiga)
asoslanadi. Induksiya arifmetik va geometrik
progressiya formulalarini, logarifmlarni oʻrganishda
uchraydigan formulalarni, Nyuton
binomi va kombinatorikaga doir formulalarni chiqarish va
boshqa xollarda keng qoʻllanadi.

 1^n+2^n+3^n+...+k^n shakldagi misollar turlari
4. 15
+ 25
+ 35
+ … + k5
5. 16
+ 26
+ 36
+ … + k6
6. 17
+ 27
+ 37
+ … + k7
….

 Misollarning ishlanish formulalari.
Masalan 12
+ 22
+ 32
+ … + k2
shunday misolni
olaylik.
Bu misolni mana bu formula orqali javobini
chiqarsak boʻladi:
𝟏𝟐 + 𝟐𝟐 + 𝟑𝟐 + … + 𝒏𝟐 =
𝒏(𝒏 + 𝟏)(𝟐𝒏 + 𝟏)
𝟔

 Misollarning ishlanish formulalari 2
Endi esa 13
+ 23
+ 33
+ … + k3
shunday misolni
olaylik.
Bu misolni mana yana shunga oʻxshash formula
orqali javobini chiqarsak boʻladi:
𝟏𝟑
+ 𝟐𝟑
+ 𝟑𝟑
+ … + 𝒏𝟑
=
𝒏 𝒏 + 𝟏
𝟐
𝟐

𝟏𝟑
+ 𝟐𝟑
+ 𝟑𝟑
+ … + 𝒏𝟑
shakldagi misol uchun
formulaning isboti
𝟏𝟑
+ 𝟐𝟑
+ 𝟑𝟑
+ … + 𝒏𝟑
=
𝒏 𝒏 + 𝟏
𝟐
𝟐
Masalan, n sonini 2 ga teng deb olaylik va misolni shu 2
qiymat qoʻygan holda ishlab ko’raylik:
Formulani isbotlashni eng oson usullaridan biri bu
nomaʻlum hadga qiymat berib ko’rish

𝟏𝟑
+ 𝟐𝟑
+ 𝟑𝟑
+ … + 𝒏𝟑
shakldagi misol uchun
formulaning isboti
𝟏𝟑 + 𝟐𝟑 + 𝟑𝟑 = 1 + 8 + 27 = 36
𝒏 𝒏+𝟏
𝟐
𝟐
=
𝟑 𝟑+𝟏
𝟐
𝟐
=
𝟏𝟐
𝟐
𝟐
=𝟔𝟐=36
Demak, biz bu yechim orqali biz formulani isbotladik.

𝟏𝐧
+ 𝟐𝐧
+ 𝟑𝐧
+ … + 𝐤𝐧
shakldagi yigʻindilarni hisoblash
uchun formula yaratish
7-03-1 Kamoldinov Doniyor

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Math answers of smth

1. 𝟏𝐧 + 𝟐𝐧 + 𝟑𝐧 + … + 𝐤𝐧 shakldagi yigʻindilarni hisoblash uchun formula yaratish 7-03-1 Kamoldinov Doniyor

2.  REJA:  Induksiya nima? 1n + 2n + 3n + … + kn shakldagi misollar turlari.  Misollarning ishlanish formulalari.  Formulalar kelib chiqishi.

3. 𝑰𝑵𝑫𝑼𝑲𝑺𝑰𝒀𝑨 𝒏𝒊𝒎𝒂? Induksiya (matematikada) — muhim isbotlash usullaridan biri; matematik induksiya aksiomasiga (prinsipiga) asoslanadi. Induksiya arifmetik va geometrik progressiya formulalarini, logarifmlarni oʻrganishda uchraydigan formulalarni, Nyuton binomi va kombinatorikaga doir formulalarni chiqarish va boshqa xollarda keng qoʻllanadi.

4.  1^n+2^n+3^n+...+k^n shakldagi misollar turlari 4. 15 + 25 + 35 + … + k5 5. 16 + 26 + 36 + … + k6 6. 17 + 27 + 37 + … + k7 ….

5.  Formula kelib chiqishi

6.  Formula kelib chiqishi

7.  Misollarning ishlanish formulalari. Masalan 12 + 22 + 32 + … + k2 shunday misolni olaylik. Bu misolni mana bu formula orqali javobini chiqarsak boʻladi: 𝟏𝟐 + 𝟐𝟐 + 𝟑𝟐 + … + 𝒏𝟐 = 𝒏(𝒏 + 𝟏)(𝟐𝒏 + 𝟏) 𝟔

8.  Misollarning ishlanish formulalari 2 Endi esa 13 + 23 + 33 + … + k3 shunday misolni olaylik. Bu misolni mana yana shunga oʻxshash formula orqali javobini chiqarsak boʻladi: 𝟏𝟑 + 𝟐𝟑 + 𝟑𝟑 + … + 𝒏𝟑 = 𝒏 𝒏 + 𝟏 𝟐 𝟐

9. 𝟏𝟑 + 𝟐𝟑 + 𝟑𝟑 + … + 𝒏𝟑 shakldagi misol uchun formulaning isboti 𝟏𝟑 + 𝟐𝟑 + 𝟑𝟑 + … + 𝒏𝟑 = 𝒏 𝒏 + 𝟏 𝟐 𝟐 Masalan, n sonini 2 ga teng deb olaylik va misolni shu 2 qiymat qoʻygan holda ishlab ko’raylik: Formulani isbotlashni eng oson usullaridan biri bu nomaʻlum hadga qiymat berib ko’rish

10. 𝟏𝟑 + 𝟐𝟑 + 𝟑𝟑 + … + 𝒏𝟑 shakldagi misol uchun formulaning isboti 𝟏𝟑 + 𝟐𝟑 + 𝟑𝟑 = 1 + 8 + 27 = 36 𝒏 𝒏+𝟏 𝟐 𝟐 = 𝟑 𝟑+𝟏 𝟐 𝟐 = 𝟏𝟐 𝟐 𝟐 =𝟔𝟐=36 Demak, biz bu yechim orqali biz formulani isbotladik.

11. Eʻtiboringiz uchun rahmat!

12. 𝟏𝐧 + 𝟐𝐧 + 𝟑𝐧 + … + 𝐤𝐧 shakldagi yigʻindilarni hisoblash uchun formula yaratish 7-03-1 Kamoldinov Doniyor