## 400 Reputation

15 years, 71 days

## what are the best values of \$m\$ and \$n\$...

Maple

help me here:

suppose we have:

h(x):=(x^n)/(sqrt(1+x^m))-log(1+x):

how can we find the best values of m and n such that h(x) > 0

one can show that for m = n = 1

h(x) > 0.

one may solve this by first finding the derivative of h(x)

diff(h(x),x)

and then solving

solve(diff(h(x),x),[m,n] )> 0

we may assume x > 0

## what is pattern in this series...

Maple

-1 / 6 + 1 / 20 - 5 / 84 + 7 / 216 - 47 / 1320 + 37 / 1560 - 319 / 12600 + 533/ 28560 - 1879 / 95760 + 1627 / 105840 --...

thanks

## how to simplify diff:...

Maple

can we simplify the answer of the following command:

diff(arctan(sqrt(b*a)/b)/sqrt(b*a), `\$`(b, n))

thanks

## how to compute this sum...

Maple

how can we find:

sum((5/2+2310*n^5+5775*n^4+5019*n^3+(3507/2)*n^2+(409/2)*n)/(27720*n^7+97020*n^6+132300*n^5+88200*n^4+29400*n^3+4410*n^2+210*n), n = 1 .. n-1)

Maple is giving answer which is very complex

## how to simplify it...

Maple

we want to find:-

sum((5/2+25*n^2+25*n)/(300*n^4+600*n^3+360*n^2+60*n), n = 1 .. n-1)

maple gives me an answer which looks complex to me? can we simplify it further?

thanks

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