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These are questions asked by max125

I would like to factor an algebraic expression that contains exponentials.
Maple spits it back unfactored. Did I enter it wrong?

factor(exp(4*y) + 2*exp(2*y) + 1);

I would like to factor


which I would like to output 14*(7 - 2*sqrt(7)),

but Maple keeps returning 98 - 28*sqrt(7).
I have a double about this alternating series.
According to maple this series converges:


However limit ln(n)/n + 1 does not equal to zero, it equals 1. Therefore the series should diverge.

Also while I am on the subject of series and limits, why is limit (-1)^n  as n goes to infinity a range between -1-I and 1 + I.

limit((-1)^(n), n=infinity)
                        -1 - I .. 1 + I



I am interested in finding the lower Riemann sum for a partition of unequal width.

The points of the partition are P = { -1, -1/4, 1/4, 3/4, 1} , and the function is f(x) = x^2.

My attempt:

restart: with(Student[Calculus1]):
RiemannSum(x^2,x={[ -1,-1/4],[-1/4, 1/4],[1/4,3/4],[3/4,1]},method=lower)

It said error range must be specified. I looked at the help page but I didnt find a specific command for entering partition points manually.


The problem is to find a100 for a sequence defined as follows. I tried the following command for a recursive sequence.
(I used 10 instead of 100 to test run it).

for n from 2 to 10 do a||n:=2*sum( a||i ,i=1..n)^2/(2*sum( a||i ,i=1..n)-1); od;

This approach did not work. It says "error recursive assignment"

Any ideas how to get a(100), also if its possible how to solve the recursive sequence explicitly.

I tried rsolve :

rsolve({ f(n)=(2*sum(f(i),i=1..n)^2/(2*sum(f(i),i=1..n)-1)),f(1)=1},f(n))
rsolve({ f(n)=(2*sum(f(i),i=1..n)^2/(2*sum(f(i),i=1..n)-1)),f(1)=1},f(n))

It just returned back the expression inertly.


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