Question

derive an explicit formula for this sum

Answer 1

\[\sum_{i=0}^{n}(n ^{n-i} 4^{i})\]

Answer 2

@ganeshie8 @waterineyes

Answer 3

so hard T_T

Answer 4

Is this not the explicit formula itself?

Answer 5

derive the formula without sum symbol

Answer 6

like find f(n) that represent this sum

Answer 7

put the values of \(i\) one by one:

\[\sum_{i=0}^{n}(n ^{n-i} 4^{i}) = 4^0 n^{n-0} + 4^1 n^{n-1} + 4^2 n^{n-2} + .... + 4^n\]

Answer 8

yea, but how do you find an equation, that you can just plug in n, and gives you the answer @_@

Answer 9

So, basically we have this.. :)

Answer 10

Have patience, I also don't know.. :P

Answer 11

fak :x

Answer 12

OMG I KNOW

Answer 13

Using Binomial?

Answer 14

it's equal to the sum of \[2^{n-i}*2^{2i} = 2^{n+i}\]

Answer 15

really? but how?

Answer 16

@ganeshie8

Answer 17

you just transform 4^i into 2^2i :P

Answer 18

ok i got the answer :D