Question

Finding coefficients of a series expansion

Answer 1

1/(1+2t) = \[\sum_{0}^{\infty} c _{k}t ^{k} = c _{0} + c _{1}t + c _{2}t ^{2} + c _{3}t ^{2} + ....\]

Answer 2

How would I go about finding c_0 up to c_3?

Answer 3

hello ...

Answer 4

depends on what your values of t is
if |2t|<1, then
1/(1+2t) can be expanded geometrically

Answer 5

since you have converging sequence in t,
1/(1 + 2t) = 1/(1 - (-2t)) = 1 + (-2t) + (-2t)^2 + (-2t)^3 + ...

Answer 6

I will have to find t later,
-R <t < R

Answer 7

R = 1/2, it's radius of convergence

Answer 8

Cool. So all the coefficients asked for are 1?

Answer 9

nvm!! its 1, -2, 4, -8?

Answer 10

ok
...

Answer 11

Haha thanks i was not thinking of the expansion you mentioned

Answer 12

yw