Exercise 7.1 Class 11 Maths Mathematical Induction| Ex 7.1 Class 11 KPK Board Mathematical Induction
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Exercise 7.1 Class 11 Maths
Exercise 7.1 Class 11 Maths Mathematical Induction| Ex 7.1 Class 11 KPK Board Maths Mathematical Induction | Study With Me
00:09:11 Intro
00:07:18 Q1
00:12:11 Q2
00:16:39 Q3
00:19:41 Q4
00:23:22 Q5
00:27:15 Q6
00:30:34 Q7
00:34:33 Q8
00:35:45 Q9
00:41:38 Q10
00:45:24 Q11
00:48:56 Q12
00:57:09 Q13
01:04:21 Q14
01:15:17 Q15
Establish the formulas given below by mathematical Induction
Q1. 2 + 4 + 6 + . . . + 2n = n(n+1)
Q2. 1 + 5 + 9 + . . . + (4n-3) = n(2n-1)
Q3. 3 + 6 + 9 + . . . + 3n = 3n(n+1) / 2
Q4. 3 + 7 + 11 + . . . + (4n-1) = n(2n+1)
Q5. 13 + 23 + 33 + . . . + n3 = [n(n+1)/2]^2
Q6. 1(1!) + 2(2!) + 3(3!) + . . . + n(n!) = (n+1)! - 1
Q7. 1.2 + 2.3 + 3.4 +...+ n(n+1) = n(n+1)(n+2) / 2
Q8. 1 +2 +22 +23 + . . . + 2n-1 = 2n-1
Q9. 1/3 +1/9 +1/27 + . . . + 1/3n = ½(1 – 1/3n)
Q10. 5C5 + 6C5 + 7C5 +…+ n+4C5 = n+5C6
Q11. 2C2 + 3C2 + 4C2 +…+ nC2 = n+1C3 for n ≥ 2
Q12. Show by mathematical induction that these are integers
(i) (52n - 1)/ 24
(ii) (10n-1 - 9n - 10) / 81
Q13
(i) 2n is greater than n for all n element of N
(ii) n! is greater than n2 for every integer n ≥ 4
Q14
(i) Show that 5 is a factor of 32n-1 + 22n-1 where n is any positive integer
(ii) Prove that 22n-1 is a multiple of 3 for all positive integers
Q15 Show that a + b is a factor of an- bn for all even positive integer n.
Exercise 7.1 Maths Class 11 KPK Book
Exercise 7.1 Maths Class 11 KPK Board
Exercise 7.1 Maths Class 11 Federal Board
Class 11 Mathematical Induction
Exercise 7.1 maths class 11 kpk board book Mathematical Induction Federal Board
Ex 71 maths class 11 kpk board book Mathematical Induction
Ex 7.1 class 11 maths Mathematical Induction kpk book
Class 11 maths ch 7 ex 7.1 Mathematical Induction
Exercise 7.1 class 11 maths Mathematical Induction
Chapter 7 maths class 11 exercise 7.1
Ex 7.1 Questions 1
Ex 7.1 Questions 2
Ex 7.1 Questions 3
Ex 7.1 Questions 4
Ex 7.1 Questions 5
Ex 7.1 Questions 6
Ex 7.1 Questions 7
Ex 7.1 Questions 8
Ex 7.1 Questions 9
Ex 7.1 Questions 10
Ex 7.1 Questions 11
Ex 7.1 Questions 12
Ex 7.1 Questions 13
Ex 7.1 Questions 14
Ex 7.1 Questions 15
Exercise 7.1 Questions 1
Exercise 7.1 Questions 2
Exercise 7.1 Questions 3
Exercise 7.1 Questions 4
Exercise 7.1 Questions 5
Exercise 7.1 Questions 6
Exercise 7.1 Questions 7
Exercise 7.1 Questions 8
Exercise 7.1 Questions 9
Exercise 7.1 Questions 10
Exercise 7.1 Questions 11
Exercise 7.1 Questions 12
Exercise 7.1 Questions 13
Exercise 7.1 Questions 14
Exercise 7.1 Questions 15
Class 11 ex 7.1 solution
Ex 7.1 class 11
Exercise 7.1 Maths Class 11
Exercise 7.1 Class 11 Maths
Exercise 7.1 Class 11 Maths KPK Board
Exercise 7.1 Class 11 Maths KPK Book
#Exercise7.1 #MathsUnit7 #KPKBoard #MathematicalInduction #Class11 #FederalBoard #FBISE #Unit7Exercise7.1 #Ex7.1MathsClass11 #Class11Maths #MathsClass11 #ProveusingMathematicalInduction #ProveanInteger #Hypothesis #Isafactorof #Isamultipleof @studywithmeinpakistan
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00:09:11 Intro
00:07:18 Q1
00:12:11 Q2
00:16:39 Q3
00:19:41 Q4
00:23:22 Q5
00:27:15 Q6
00:30:34 Q7
00:34:33 Q8
00:35:45 Q9
00:41:38 Q10
00:45:24 Q11
00:48:56 Q12
00:57:09 Q13
01:04:21 Q14
01:15:17 Q15
Establish the formulas given below by mathematical Induction
Q1. 2 + 4 + 6 + . . . + 2n = n(n+1)
Q2. 1 + 5 + 9 + . . . + (4n-3) = n(2n-1)
Q3. 3 + 6 + 9 + . . . + 3n = 3n(n+1) / 2
Q4. 3 + 7 + 11 + . . . + (4n-1) = n(2n+1)
Q5. 13 + 23 + 33 + . . . + n3 = [n(n+1)/2]^2
Q6. 1(1!) + 2(2!) + 3(3!) + . . . + n(n!) = (n+1)! - 1
Q7. 1.2 + 2.3 + 3.4 +...+ n(n+1) = n(n+1)(n+2) / 2
Q8. 1 +2 +22 +23 + . . . + 2n-1 = 2n-1
Q9. 1/3 +1/9 +1/27 + . . . + 1/3n = ½(1 – 1/3n)
Q10. 5C5 + 6C5 + 7C5 +…+ n+4C5 = n+5C6
Q11. 2C2 + 3C2 + 4C2 +…+ nC2 = n+1C3 for n ≥ 2
Q12. Show by mathematical induction that these are integers
(i) (52n - 1)/ 24
(ii) (10n-1 - 9n - 10) / 81
Q13
(i) 2n is greater than n for all n element of N
(ii) n! is greater than n2 for every integer n ≥ 4
Q14
(i) Show that 5 is a factor of 32n-1 + 22n-1 where n is any positive integer
(ii) Prove that 22n-1 is a multiple of 3 for all positive integers
Q15 Show that a + b is a factor of an- bn for all even positive integer n.
Exercise 7.1 Maths Class 11 KPK Book
Exercise 7.1 Maths Class 11 KPK Board
Exercise 7.1 Maths Class 11 Federal Board
Class 11 Mathematical Induction
Exercise 7.1 maths class 11 kpk board book Mathematical Induction Federal Board
Ex 71 maths class 11 kpk board book Mathematical Induction
Ex 7.1 class 11 maths Mathematical Induction kpk book
Class 11 maths ch 7 ex 7.1 Mathematical Induction
Exercise 7.1 class 11 maths Mathematical Induction
Chapter 7 maths class 11 exercise 7.1
Ex 7.1 Questions 1
Ex 7.1 Questions 2
Ex 7.1 Questions 3
Ex 7.1 Questions 4
Ex 7.1 Questions 5
Ex 7.1 Questions 6
Ex 7.1 Questions 7
Ex 7.1 Questions 8
Ex 7.1 Questions 9
Ex 7.1 Questions 10
Ex 7.1 Questions 11
Ex 7.1 Questions 12
Ex 7.1 Questions 13
Ex 7.1 Questions 14
Ex 7.1 Questions 15
Exercise 7.1 Questions 1
Exercise 7.1 Questions 2
Exercise 7.1 Questions 3
Exercise 7.1 Questions 4
Exercise 7.1 Questions 5
Exercise 7.1 Questions 6
Exercise 7.1 Questions 7
Exercise 7.1 Questions 8
Exercise 7.1 Questions 9
Exercise 7.1 Questions 10
Exercise 7.1 Questions 11
Exercise 7.1 Questions 12
Exercise 7.1 Questions 13
Exercise 7.1 Questions 14
Exercise 7.1 Questions 15
Class 11 ex 7.1 solution
Ex 7.1 class 11
Exercise 7.1 Maths Class 11
Exercise 7.1 Class 11 Maths
Exercise 7.1 Class 11 Maths KPK Board
Exercise 7.1 Class 11 Maths KPK Book
#Exercise7.1 #MathsUnit7 #KPKBoard #MathematicalInduction #Class11 #FederalBoard #FBISE #Unit7Exercise7.1 #Ex7.1MathsClass11 #Class11Maths #MathsClass11 #ProveusingMathematicalInduction #ProveanInteger #Hypothesis #Isafactorof #Isamultipleof @studywithmeinpakistan
Note: This Channel is for Education Purpose Only.
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