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Let $f: N -> N$ be a fucntion satisfying $f(n+m) = f(n) + f(m)$ for all $m$ and $n$. Prove that there exist a constant $c$ so that $f(n) = cn$.

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Prove that $im(T^{k+1}) ⊆ im(T^k)$ for every non-negative integer $k$ for any linear transformation $T: R^n → R^n$

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∀n∈ℕ:∑(-1)^(k+1)(1/k) [from k=1 to 2n] = ∑1/(n+k) [from k=1 to n]

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List Question

Prove $a_n < 2^n$ using strong induction

Can we do the inductive step without using inductive hypothesis

Prove by Induction of a Total Function

Let $f: N -> N$ be a fucntion satisfying $f(n+m) = f(n) + f(m)$ for all $m$ and $n$. Prove that there exist a constant $c$ so that $f(n) = cn$.

Proof by induction: $3^n > n^2$ for all integers greater or equal to 1

Proof inequality and series using Induction

Mathematical Induction for a C++ loop

Proof by induction: inequality $n! > n^3$ for $n > 5$

Mathematical Induction Problem solving

Prove the following with Induction

Show by induction: $(1+\frac{1}{n})^{n}<n$

Prove that $im(T^{k+1}) ⊆ im(T^k)$ for every non-negative integer $k$ for any linear transformation $T: R^n → R^n$

∀n∈ℕ:∑(-1)^(k+1)(1/k) [from k=1 to 2n] = ∑1/(n+k) [from k=1 to n]

Upper bound on a sequence after a finite number of steps

Induction proof for integrals

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