Induction - Problem Solving Practice Problems Online

Consider a statement $S(N): 1+3+5+\cdots+(2N-1)=7+N^2,$ then which of the following is true?

What is the remainder when ${105}^{165}-1$ is divided by 4?

Consider a sequence $\{a_n\}$ with $a_1=5$ and $a_2=13.$ If the sequence satisfies $a_{n+2}=5a_{n+1}-6a_n$ for all positive integers $n,$ what is $a_{50}?$

If $\displaystyle a_n=2^{2^n}+1$ for $n > 1,$ then what is the last digit of $a_{451}?$

Let $P(n)$ be a statement involving a positive integer $n.$ $P(n+2)$ is true if $P(n)$ or $P(n+1)$ is true. Then what is the sufficient condition for the statement $P(n)$ to be true for all positive integers?

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Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Problem Solving Skills

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Induction - Problem Solving

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.