Can anyone show me how to simplify this fraction:(k+1)((k+1)+1)(2(k+1)+1)6;.What can be factored out and so forth?Thanks.

(k+1)((k+1)+1)(2(k+1)+1)6=(k+1)(k+2)(2k+3)6Then if&nbsp;k=2n&nbsp;you have(k+1)(k+2)(2k+3)6=(2n+1)(2n+2)(4n+3)6=(2n+1)2(n+1)(4n+3)6=(2n+1)(n+1)(4n+3)3it's not so different if&nbsp;k=2n+1. Then if you want you can consider in more detail: what if&nbsp;n=2m? And&nbsp;n=2m+1? Enjoy!

Question: "Can anyone show me how to simplify this..."

High School
Algebra
Pre-Algebra
Fractions

Jordan Chavez

Answered question

2022-03-17

Can anyone show me how to simplify this fraction:

\frac{(k + 1) ((k + 1) + 1) (2 (k + 1) + 1)}{6}; .

What can be factored out and so forth?
Thanks.

Answer & Explanation

Vaspplado8ko

Beginner2022-03-18Added 5 answers

$\frac{(k + 1) ((k + 1) + 1) (2 (k + 1) + 1)}{6} = \frac{(k + 1) (k + 2) (2 k + 3)}{6}$
Then if $k = 2 n$ you have
$\frac{(k + 1) (k + 2) (2 k + 3)}{6} = \frac{(2 n + 1) (2 n + 2) (4 n + 3)}{6}$
$= \frac{(2 n + 1) 2 (n + 1) (4 n + 3)}{6}$
$= \frac{(2 n + 1) (n + 1) (4 n + 3)}{3}$
it's not so different if $k = 2 n + 1$ . Then if you want you can consider in more detail: what if $n = 2 m$ ? And $n = 2 m + 1$ ? Enjoy!

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Which expression has both 8 and n as factors???
One number is 2 more than 3 times another. Their sum is 22. Find the numbers
8, 14
5, 17
2, 20
4, 18
10, 12
Perform the indicated operation and simplify the result. Leave your answer in factored form
$[\frac{(4 x - 8)}{(- 3 x)}] . [\frac{12}{(12 - 6 x)}]$
An ordered pair set is referred to as a ___?
Please, can u convert 3.16 (6 repeating) to fraction.
Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.
A) $6 - \frac{x}{3} = 2$
B) $\frac{x}{3} - 6 = 2$
C) 3x−6=2
D) $\frac{3}{x} - 6 = 2$
Find: $2.48 \div 4$ .
Multiplication $999 \times 999$ equals.
Solve: (128÷32)÷(−4)=
A) -1
B) 2
C) -4
D) -3
What is $0.78888 ... . .$ converted into a fraction? $(0.7 \bar{8})$
The mixed fraction representation of 7/3 is...
How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?
Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.
A)235.47,7
B)235.047,4
C)235.47,4
D)234.057,7
Find four equivalent fractions of the given fraction: $\frac{6}{12}$
How to find the greatest common factor of $80 x^{3}, 30 y x^{2}$ ?

Didn't find what you were looking for?