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Chapter 4: Principle of Mathematical Induction

NCERT Solutions for CBSE Class 10 Mathematics — 4 solved questions with detailed explanations.

4
Questions
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Topics

Solved Questions

Q1. The first step in mathematical induction is to:

Difficulty: Easy · Topic: PMI

Solution

Step 1 (Base case): Verify P(1) is true. Step 2 (Inductive step): Assume P(k) true, prove P(k+1).

Q2. 1 + 2 + 3 + ... + n equals:

Difficulty: Easy · Topic: Sum Formulas

Solution

Sum of first n natural numbers = n(n+1)/2. Proved by induction or by Gauss's method.

Q3. 1²+2²+...+n² =

Difficulty: Easy-Medium · Topic: Principle of Mathematical Induction

Solution

n(n+1)(2n+1)/6.

Q4. 1³+2³+...+n³ =

Difficulty: Easy-Medium · Topic: Principle of Mathematical Induction

Solution

[n(n+1)/2]².

Other Chapters in Mathematics

Ch 1: SetsCh 2: Relations & FunctionsCh 3: Trigonometric FunctionsCh 5: Complex NumbersCh 6: Linear InequalitiesCh 7: Permutations & CombinationsCh 8: Binomial TheoremCh 9: Sequences & SeriesCh 10: Straight LinesCh 11: Conic SectionsCh 12: Intro to 3D GeometryCh 13: Limits & DerivativesCh 14: Mathematical ReasoningCh 15: StatisticsCh 16: Probability

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