Complete Theory

Worked Examples

Example 1Induction — sum of

k(k+1)

Example 2Coefficient in binomial expansion

Exercise 1InductionMedium

📋 Problem to solve

Prove by induction that

\sum_{k=1}^n (2k-1) = n^2

for all

n\in\mathbb{N}

Exercise 2Binomial expansionMedium

📋 Problem to solve

Expand

(x-2)^5

using the binomial theorem.

Exercise 3Sum of squaresHard

📋 Problem to solve

Prove by induction that

\sum_{k=1}^n k^2 = n(n+1)(2n+1)/6

📚

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