Simple sigma equation written into a nth term sequence, now how do we make a new equation that will instantly add them all up? (This isnt H.W. we really just want to know haha) e.g.
1 + 3 + 5 + 7 + 9 + ... + (2n - 1) = n^2
Simple right?? So how would we find the pattern for this equation??
2 + 8 + 24 + ... + n(2^n) = ???
THANX! :D
1 + 3 + 5 + 7 + 9 + ... + (2n - 1) = n^2
Simple right?? So how would we find the pattern for this equation??
2 + 8 + 24 + ... + n(2^n) = ???
THANX! :D
-
It's a bit messy, but for the derivation, see sources. The bottom line is:
Sum from 0 to n of n(2^n) = 2[1 + n * 2^(n+1) - (n+1)2^n]
Note that the sum from 0 to n is the same as the sum from 1 to n.
Sum from 0 to n of n(2^n) = 2[1 + n * 2^(n+1) - (n+1)2^n]
Note that the sum from 0 to n is the same as the sum from 1 to n.