Question

Find the general term, An, for the following infinite series. SEE BELOW

Answer 1

\[\frac{ 4 }{ 1^{2}+1 }, \frac{ 1 }{ 2^{2}+1 }, \frac{ 4 }{ 3^{2}+1 }+...\]

Answer 2

with n starting at 1

Answer 3

so far I have \[\frac{ ? }{ n^{2}+1 }\]

Answer 4

I just don't know how to represent the oscillating 4, 1, 4 1... numerator

Answer 5

I figure it has something to do with maybe 4^1 and 4^0

Answer 6

that is what i was thinking too

Answer 7

maybe try something like \(4-3(-1)^k\)

Answer 8

no that doesn't work

Answer 9

how about
\[\frac{5}{2}+\frac{3}{2}\times (-1)^k\]

Answer 10

or if you are starting at \(k=1\) with \(4\) then adjust to
\[\frac{5}{2}-\frac{3}{2}\times (-1)^k\]

Answer 11

awesome ill try that. thanks!

Answer 12

yw

Answer 13

satellite can you help me with my problem?