Question

How can I simplify this series?

sum_{n=0}^{infty}5x(n+r)(n+r-1)c _{n}x ^{n+r-2}+sum_{n=0}^{infty}(7x-6)(n+r)c _{n}x ^{n+r-1}-sum_{n=0}^{infty}(6)c _{n}x ^{n+r} How can I simplify this series?

sum_{n=0}^{infty}5x(n+r)(n+r-1)c _{n}x ^{n+r-2}+sum_{n=0}^{infty}(7x-6)(n+r)c _{n}x ^{n+r-1}-sum_{n=0}^{infty}(6)c _{n}x ^{n+r} @Mathematics

Answer 1

\[\sum_{n=0}^{\infty}5x(n+r)(n+r-1)c _{n}x ^{n+r-2}+\sum_{n=0}^{\infty}(7x-6)(n+r)c _{n}x ^{n+r-1}-\sum_{n=0}^{\infty}(6)c _{n}x ^{n+r}\]

Unfortunately, it won't do it symbolically in the first post.

Answer 2

\[\sum_{n=0}^{\infty}5x(n+r)(n+r-1)c _{n}x ^{n+r-2}\]
\[+\sum_{n=0}^{\infty}(7x-6)(n+r)c _{n}x ^{n+r-1}-\sum_{n=0}^{\infty}(6)c _{n}x ^{n+r} \]

Answer 3

? that's what I put in.

Answer 4

i know i was just typing it so i could read it. but i have no idea what do to here

Answer 5

me neither. it's not just for the series, i'm needing to simplify the series to get the answer to a bigger problem

Answer 6

yeah i figured it was on the way to something

Answer 7

it's actually to solve a differential equation ;)

Answer 8

ick

Answer 9

of second degree

Answer 10

at least it's homogeneous

Answer 11

and geometric

Answer 12

good luck!

Answer 13

:D thanks