Binomial Questions (1 Viewer)

[Premus]

Hey

I have a few questions id like to clear up.

1. for finding the greatest coefficient of binomal expansions:
you let T (k+1 ) / T (k) >= 1
but once i solve for k, im not sure what 'k' to select....
eg:

(2+ 5x ) ^ 11 when x = 1.5

in the end you get k <= 9.47 , from this how do u determine what value of k to choose?? i get really confused here!

2. use ( 1 + x ) ^ n to show that

1 - 1/2 nC1 + 1/3 nC2 - 1/4 nC3 +.......+ (-1)^n / n+1 * nCn = 1/ n+1

for this i integrated both sides , substituted x = 0 to get C , which = 1/n+1
then i substituted x = -1 , but didnt get the exact answer...

3. what is the last term of the expansion ( 1+ x ) ^ 2n

Thanks

 

[Xayma]

2. &int; w.r.t.x

3. ax^n-1xⁿ⁺¹/a, a&ne;0

 

[mojako]

1. http://www.boredofstudies.org/community/showpost.php?p=886455&postcount=5
2. c = - 1/n+1
3. ²ⁿC_2n*x²ⁿ*1^2n-2n
which of course simplifies to x²ⁿ
so does Xayma's solution,
except his is more elegant
u shud really use his method.
no dont use it <==

 

[tennille]

Choose 9 because it is less than or equal to 9.47 (clearly, there is no such thing as the 10.47th term). If it said k is less than or equal to 4, then the value of k would be 4 and 3.

 

[grimreaper]

Choose 9 because it is less than or equal to 9.47 (clearly, there is no such thing as the 10.47th term). If it said k is less than or equal to 4, then the value of k would be 4 and 3.

yes k = 9 however it is the tenth term that your after since it is T (k+1 ) which has the largest coefficent