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Principle of Mathematical Induction

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Motivation

Subtopic

Motivation under Principle of Mathematical Induction for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Mathematical induction effectively proves that a property is ———— by the set of natural numbers.

    A.

    Inherited

    B.

    Rejected

    C.

    Divided

    D.

    Subtracted

  2. 2.

    If P(n)P(n) involves an inequality like an<bna_n < b_n, the goal of the inductive step is to show:

    A.

    ak+1=bk+1a_{k+1} = b_{k+1}

    B.

    ak+1<bk+1a_{k+1} < b_{k+1} using the fact ak<bka_k < b_k

    C.

    ak<ak+1a_k < a_{k+1}

    D.

    bk<bk+1b_k < b_{k+1}

  3. 3.

    Why can we not use induction to prove a statement for all negative integers …,−3,−2,−1\dots, -3, -2, -1 using the standard base case n=1n=1?

    A.

    Negative integers are not numbers

    B.

    Standard induction moves in the positive direction from a starting point

    C.

    Induction only works for primes

    D.

    Negative numbers don't have successors

Download the worksheet for Principle of Mathematical Induction - Motivation to practice offline. It includes additional chapter-level practice questions.

The Principle of Mathematical Induction

Subtopic

The Principle of Mathematical Induction under Principle of Mathematical Induction for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the common difference between terms in the sum 1+4+7+⋯+(3n−2)1 + 4 + 7 + \dots + (3n-2)?

    A.

    1

    B.

    2

    C.

    3

    D.

    4

  2. 2.

    In the statement P(n):1+2+22+⋯+2n−1=2n−1P(n): 1 + 2 + 2^2 + \dots + 2^{n-1} = 2^n - 1, what is the term for n=3n=3 on the LHS?

    A.

    232^3

    B.

    222^2

    C.

    323^2

    D.

    3

  3. 3.

    If P(n)P(n) is a statement such that P(1)P(1) is true and P(k)  ⟹  P(k+1)P(k) \implies P(k+1), then P(n)P(n) is true for:

    A.

    All n∈Zn \in \mathbb{Z}

    B.

    All n∈Nn \in \mathbb{N}

    C.

    All n∈Rn \in \mathbb{R}

    D.

    Only even nn

Download the worksheet for Principle of Mathematical Induction - The Principle of Mathematical Induction to practice offline. It includes additional chapter-level practice questions.

Simple Applications

Subtopic

Simple Applications under Principle of Mathematical Induction for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Consider P(n):2⋅7n+3⋅5n−5P(n): 2 \cdot 7^n + 3 \cdot 5^n - 5 is divisible by 24. What is the value of the expression for the base case n=1n=1?

    A.

    12

    B.

    24

    C.

    48

    D.

    10

  2. 2.

    If P(n)P(n) is the statement 22n−12^{2n} - 1, which of the following represents P(k+1)P(k+1)?

    A.

    22k−12^{2k} - 1

    B.

    22k+2−12^{2k+2} - 1

    C.

    2k+1−12^{k+1} - 1

    D.

    22k+1−12^{2k+1} - 1

  3. 3.

    In a series 1⋅3+2⋅4+3⋅5+...1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + ..., what is the expression for the kthk^{th} term?

    A.

    k(k+1)k(k+1)

    B.

    k2+1k^2 + 1

    C.

    k(k+2)k(k+2)

    D.

    (k+1)(k+2)(k+1)(k+2)

Download the worksheet for Principle of Mathematical Induction - Simple Applications to practice offline. It includes additional chapter-level practice questions.

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