Goodie1857
Goodie1857 Goodie1857
  • 19-09-2019
  • Mathematics
contestada

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.
(Hint: Write 7 = 6 + 1.)

Respuesta :

LammettHash
LammettHash LammettHash
  • 19-09-2019

By the binomial theorem,

[tex]7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1[/tex]

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

Answer Link

Otras preguntas

What are some ways that your parents or other adults have encouraged you to achieve your goals and aspirations?
How did William Bradford’s work prove to be historically significant?
Help please. Select all correct answers
what is the difference between peptide and protein​
Most of the workers who laid the Central Pacific Railroad were?
Which word can describe a person's gender identity? A) Female B) Intersexual C) Asexual D) Androgynous
Help please. Select all correct answers
Elite Coffee and Bakery, a café that offers a relaxing environment to enjoy quality coffees, teas, soups, and other menu items, has a poster in the front of its
I want to know the poem, Barter wrote by Sara Teasdale of paraphrase. Please help me...answer what you know.​
Why does Walt whiltman use the word sing