# Questions tagged [binomial-theorem]

For questions related to the binomial theorem, which describes the algebraic expansion of powers of binomials.

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### What does Euler mean when he says "Let the arc z be infinitely small ; there will be sin.z=z and cos.z=1..."?

I am referring to, specifically the sin.z=z and cos.z=1. I am reading Euler's Introductio In Analysin Infinitorium, Vol. I, Ch. VIII and he jumps from binomials to ...
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### Let $p$ be an odd prime and let $n$ be a positive integer. Use the Binomial Theorem to show that $(1+p)^{p^{n-2}}\not\equiv1$ (mod $p^n$).

The Problem: Let $p$ be an odd prime and let $n$ be a positive integer. Use the Binomial Theorem to show that $(1+p)^{p^{n-2}}\not\equiv1$ (mod $p^n$). Source: Abstract Algebra, $3^{rd}$ edition, ...
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### Having difficulties with pendulum theory and percentage error homework problem.

The pendulum theory： $$t=2 \pi \sqrt{l/g},$$ where $t$ is the time of period, $L$ is the length of the pendulum, $G$ is the acceleration due to the gravity (~9.81 m/s²). Calculate the expected ...
### how to calculate the value $0.9^{31}$
How to calculate the value of a decimal raised to a big power without a calculator. I have been using the formula $1-m x+ (m(m-1)/2!) x^2$ but this does not give the correct answer sometimes. Can ...