Hi,

A)
$\dfrac{n(2n+1)(7n+1)}{6} \\

= \dfrac{14n^3+9n^2+n}{6} \\

= \dfrac{12n^3+6n^2}{6} + \dfrac{2n^3+3n^2+n}{6} \\

=2n^3+n^2+ \dfrac{n(2n^2+3n+1)}{6} \\

= 2n^3+n^2+ \dfrac{n(n+1)(2n+1)}{6} \\

= 2n^3+n^2+ 1^2+2^2+3^2+...+n^2\ is\ an\ integer.
$

B)
Only if n=4*k or n=4*k+1 , k beeing an integer.

8 0

2 years ago

Greatest common factor of 69 and 46

exis [7]

$Greatest\ common\ factor\ is\ the\ highest\ number\ by\ witch\ 69\ and\ 46\\can\ be\ divided\\\\
69:3\\
23:23\\\\46:2\\23:23
\\\\GCF=23\\\\Greatest\ common\ factor\ of\ 69\ and\ 46 \ is\ equal\ to\ 23.
$

4 0

3 years ago

Read 2 more answers

If you bought 2 pairs of jeans that cost $19.99 each. How much change would you receive if you paid with a $50.00 bill? PLEASE H

damaskus [11]

10.02

19.99x2 is 39.98
50-39.98= 10.02

3 0

2 years ago

Read 2 more answers