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Which term is defined by the following statement?

used to demonstrate the validity of a conjecture based on the truth of a first case, the assumption of truth of a kth case, and the demonstration of truth for the (k + 1)th case
a.
sigma notation
c.
Euler’s formula
b.
mathematical induction
d.
n factorial

Sagot :

Answer:

Mathematical notation

Step-by-step explanation:

edge 2021

A statement 'used to demonstrate the validity of a conjecture based on the truth of a first case, the assumption of truth of a kth case, and the demonstration of truth for the (k + 1)th case' defines mathematical induction.

The correct answer is option (b) mathematical induction.

What is sigma notation?

"The sigma notation (Σ) is generally used to denote a sum of multiple terms."

What is Euler's formula?

In geometry,  V − E + F = 2

where, V, E, and F are the numbers of vertices, edges, and faces of any simple polyhedron

What is n factorial?

  • For a positive integer n, the n factorial is the product of all the positive numbers preceding or equivalent to n.
  • n! = n × (n-1) × . . . × 1

What is mathematical induction?

  • It is used to prove that an identity is valid for all integers  n ≥ 1 .
  • Steps to show a propositional function F(n) is true for all integers  n ≥ a, where a is a fixed integer.

        -   F(a) is true.

        -   if F(k) is true for some integer k ≥ a, then F(k + 1) is also true.

For given example,

a statement 'used to demonstrate the validity of a conjecture based on the truth of a first case, the assumption of truth of a kth case, and the demonstration of truth for the (k + 1)th case' defines mathematical induction.

Therefore, the correct answer is option (b) mathematical induction.

Learn more about mathematical induction here:

https://brainly.com/question/1333684

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