Prove that for any natural n: athe number 7^(n+4) −7^n is divisible by 30.bthe number 3^(n + 2) −2^(n +2) +3^n −2^n is divisible by 10.

a) Let ; then , which is divisible by 30. We have

and since we know , it follows that for all .

b) We can write

and we're done.

207/8 is the right

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.