Question

come up with the function f(x) whose expansion in powers of x is:

Answer 1

plz check the pic below

Answer 2

\[f(x) =n^nx^n\]
...right?

Answer 3

no i think it's should be something near x/(1-x)^2

Answer 4

this is a power series

Answer 5

sorry i meant \(\frac{x}{(1-x)^2}\)

Answer 6

no. if it's this it should be

Answer 7

i think we need integral 1/(1-x)^2 again?

Answer 8

\[\frac{x(x+1)}{(1-x)^3}\]

Answer 9

I looked at \[\sum_{k=1}^{\infty}(k+1)(k+2)x^k\]

Answer 10

integrated twice...found sum...differentiated twice

Answer 11

then expanded the above to get

\[\sum_{k=1}^{\infty}(k^2+3k+2)x^k\]


solved for \[\sum_{k=1}^{\infty}k^2x^k\]

Answer 12

can you help me on another one?

Answer 13

it looks like this

Answer 14

looks like it might be \(\displaystyle\cos\left(\frac{x}{2}\right)\)

Answer 15

i got hint like this what's this mean?