from a high school level math book "les math au carré" by M-P. Falissard , page 133

n integer

she uses the expression to deduce the limit of the sum as m approaches infinity (26)

my gratitude to any solid help on this one !

Started by zerocordas, Sep 21, 2016

2 replies to this topic

Posted 21 September 2016 - 10:24 AM

from a high school level math book "les math au carré" by M-P. Falissard , page 133

n integer

she uses the expression to deduce the limit of the sum as m approaches infinity (26)

my gratitude to any solid help on this one !

Posted 21 September 2016 - 12:23 PM

First, of course, you can factor the "2^3 = 8" out of the series: .

Second, the sum of n to a power is always a polynomial in n of degree one higher than that power.

So . Check the value for 4 different values of m to get 4 equations for a, b, c, d, and e.

For example, if m= 1, so a+ b+ c+ d+ e= 1. If m= 2, so 16a+ 8b+ 4c+ 2d+ e= 9.

Now look at m= 3 and 4 to get two more equations.

**Edited by HallsofIvy, 21 September 2016 - 12:27 PM.**

Posted 21 September 2016 - 02:24 PM

sorry for an unforgivable typo !!!!

n^3/2^n .

but even this answer was helpful. sum of the powers must be the next power , seems logical , is there a proof ?

fantastic , (n(n+1))^2 / 4 is a polynome of deg 4 indeed.

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