help!! i need help!! i dont understand this..help..please?

Question

please help i don't know how to solve this. i dont even understand this.. so please show a very detailed working so i can understand it. and if you know a site where i can learn all about this please do tell.. please..

let (a subs n) be the sequence defined by

a subs n = [ (n^2+8n+10) / (n + 9)]

where the [x] is the largest integer that does not exceed [x]. find the value of (the sum symbol: the one that looks like an E. well i t looks like an M rotated to the left by 90 degress.) oh and on top of the symbol is 30 and in the side there is (a subs n).

if you know the site where i can learn the basics for this stuff please tell me.. cuz its not making sense to me.

Answer 1

If you were to just manually add it up from n = 0 to 30, you would get 446.
Take as an example, when n = 5, that expression gives 5.357, but since you require the largest integer not exceeding that, it gives you 5. Add them all up from n = 0 to n = 30 to get 446.

If you wish to do some more analysis, you could rewrite your expression like this:
(n^2+8n+10) / (n + 9) = (n-1) + 19/(n+9)
n-1 is an integer,
19/(n+9) is a fraction
for n = 0, [19/(n+9)] = 2
for 1 <= n <= 10, [19/(n+9)] = 1
for n >= 11, [19/(n+9)] = 0

So it boils down to solving
1 + ∑ (1 to 10) {n} + ∑(11to30) {n-1}
= 1 + 10/2 (1 + 10) + 20/2 * (10+29)
= 446

Answer 2

Assuming the summation is from n=1 to 30:
sum{n=1 to 30}a_n
=sum{n=1 to 30}[ (n^2+8n+10) / (n + 9)]
=sum{n=1 to 30}[ n-1+19 / (n + 9)]
=sum{n=1 to 30}(n-1+[ 19 / (n + 9)])
=sum{n=1 to 30}(n-1)
+sum{n=1 to 30}([ 19 / (n + 9)])
=sum{n=0 to 29}(n)
+sum{n=1 to 30}([ 19 / (n + 9)])
=1/2*(29)*30
+sum{n=1 to 30}([ 19 / (n + 9)])
=435+sum{n=1 to 30}([ 19 / (n + 9)])
=435+sum{n=1 to 10}(1)
=435+10
=445

Answer 3

The "E" symbol is sigma, it denotes "sum of".

I think if you got yourself into mathematics this advanced, you should be able to figure it out yourself.