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Mathematical Induction

True or false: inductive reasoning depends on working with different cases and developing a conjecture.

a) TRUE
b) FALSE
c) MAYBE
d) None of these

✔Answer

Correct Answer Is : TRUE

Solution Is :

By principle of mathematical induction for all n ∈ N, 1∧3 + 2∧3 + 3∧3 + ……… + n∧3 =

a) N(n + 1)
b) (n(n + 1))∧2
c) (n(n + 1))∧3
d) (n(n + 1)/2)∧2

✔Answer

Correct Answer Is : (n(n + 1)/2)∧2

Solution Is :

By principle of mathematical induction for all n ∈ N, 1+ (1/(1+2)) + (1/(1+2+3)) + ……… +(1/(1+2+3+ ……. + n)) =

a) 2n / (n+1)
b) 2 / (n+1)
c) 2n / (n-1)
d) 2 / (n-1)

✔Answer

Correct Answer Is : 2n / (n+1)

Solution Is :

By principle of mathematical induction for all n ∈ N, 1.2.3+ 2.3.4 + ……… +(n(n+1)(n+2)) =

a) N(n+1)(n+2)
b) N(n+1)(n+2)(n+3)
c) N(n+1)(n+2)(n+3)/4
d) (n+1)(n+2)(n+3)/4

✔Answer

Correct Answer Is : N(n+1)(n+2)(n+3)/4

Solution Is :

By principle of mathematical induction for all n ∈ N, (2n + 7)_________ (n+3)∧2

a) Less than
b) Greater than
c) Equal to
d) Not equal to

✔Answer

Correct Answer Is : Less than

Solution Is :

By principle of mathematical induction for all n ∈ N, 41∧n - 14∧n is a _________ 27.

a) Addition of
b) Subtraction of
c) Multiple of
d) Divisible of

✔Answer

Correct Answer Is : Multiple of

Solution Is :

By principle of mathematical induction for all n ∈ N, n(n+1)(n+5) is a multiple of ___________ .

a) 2
b) 3
c) 4
d) 5

✔Answer

Correct Answer Is : 3

Solution Is :

True or false: the induction means the determination from particular cases or facts.

a) TRUE
b) FALSE
c) MAYBE
d) None of these

✔Answer

Correct Answer Is : FALSE

Solution Is :

By principle of mathematical induction for all ________, 1 + 3 + 3∧2 + ……… + 3∧(n-1) = 3∧n - 1 / 2

a) N ∈ N
b) N = N
c) N < N
d) N > N

✔Answer

Correct Answer Is : N ∈ N

Solution Is :

When the first tile is pushed in the indicated direction, all the tiles will fall is the example of:

a) Principle of mathematical induction
b) Principle of mathematical deduction
c) Principle of mathematical formulation
d) Principle of mathematical reasoning

✔Answer

Correct Answer Is : Principle of mathematical induction

Solution Is :

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Quantitative Aptitude Practice Algebra Study Material

Mathematical Induction

True or false: inductive reasoning depends on working with different cases and developing a conjecture.

Correct Answer Is : TRUE

Solution Is :

By principle of mathematical induction for all n ∈ N, 1∧3 + 2∧3 + 3∧3 + ……… + n∧3 =

Correct Answer Is : (n(n + 1)/2)∧2

Solution Is :

By principle of mathematical induction for all n ∈ N, 1+ (1/(1+2)) + (1/(1+2+3)) + ……… +(1/(1+2+3+ ……. + n)) =

Correct Answer Is : 2n / (n+1)

Solution Is :

By principle of mathematical induction for all n ∈ N, 1.2.3+ 2.3.4 + ……… +(n(n+1)(n+2)) =

Correct Answer Is : N(n+1)(n+2)(n+3)/4

Solution Is :

By principle of mathematical induction for all n ∈ N, (2n + 7)_________ (n+3)∧2

Correct Answer Is : Less than

Solution Is :

By principle of mathematical induction for all n ∈ N, 41∧n - 14∧n is a _________ 27.

Correct Answer Is : Multiple of

Solution Is :

By principle of mathematical induction for all n ∈ N, n(n+1)(n+5) is a multiple of ___________ .

Correct Answer Is : 3

Solution Is :

True or false: the induction means the determination from particular cases or facts.

Correct Answer Is : FALSE

Solution Is :

By principle of mathematical induction for all ________, 1 + 3 + 3∧2 + ……… + 3∧(n-1) = 3∧n - 1 / 2

Correct Answer Is : N ∈ N

Solution Is :

When the first tile is pushed in the indicated direction, all the tiles will fall is the example of:

Correct Answer Is : Principle of mathematical induction

Solution Is :

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