Question

Determine sum of all natural numbers 'n' such
that
(n+1)/
(n+7)
is an
integer​

Answer 1

Answer:

by simple algebraic polynomial division we get 36 as remainder

now (n+1)^2/(n+7) to be an integer 36 have to divisable by (n+7)

now 36 has 9 factors :1, 2, 3, 4, 6, 9, 12, 18 and 36

and only 4 factors are greater then 7 : 9, 12, 18, 36

so there are 4 natural numbers n such that (n+1)^2/(n+7) is an integer.

n =(9-7) = 2 or,

=(12-7)= 5 or,

=(18-7)= 11 or,

=(36-7)= 29

like:

when n=2

(n+1)^2/(n+7)=3^2/9=1 is an integer

when n=5

(n+1)^2/(n+7)=6^2/12=3 is an integer

when n=11

(n+1)^2/(n+7)=12^2/18=8 is an integer

when n=29

(n+1)^2/(n+7)=30^2/36=25 is an integer

so option (i) is correct

there are 4 such numbers

Answer 2

Answer mark as brainliest

Step-by-step explanation:determine all natural numbers n such that(n+1),(n+7) is an integer. ... that(n+1)/(n+. Related Answer. For all positive integer n , prove that n77+n55+23n3-n105 is an integer ... The sum of all natural numbers 'n' such that 100 lt n lt 200