  We perform fluctuation analyses on the data from the Spitzer GOODS survey
(epoch one) in the Hubble Deep Field North (HDF-N). We fit a parameterised
power-law number count model of the form dN/dS = N_o S^{-\delta} to data from
each of the four Spitzer IRAC bands, using Markov Chain Monte Carlo (MCMC)
sampling to explore the posterior probability distribution in each case. We
obtain best-fit reduced chi-squared values of (3.43 0.86 1.14 1.13) in the four
IRAC bands. From this analysis we determine the likely differential faint
source counts down to $10^{-8} Jy$, over two orders of magnitude in flux
fainter than has been previously determined.
  From these constrained number count models, we estimate a lower bound on the
contribution to the Infra-Red (IR) background light arising from faint
galaxies. We estimate the total integrated background IR light in the Spitzer
GOODS HDF-N field due to faint sources. By adding the estimates of integrated
light given by Fazio et al (2004), we calculate the total integrated background
light in the four IRAC bands. We compare our 3.6 micron results with previous
background estimates in similar bands and conclude that, subject to our
assumptions about the noise characteristics, our analyses are able to account
for the vast majority of the 3.6 micron background. Our analyses are sensitive
to a number of potential systematic effects; we discuss our assumptions with
regards to noise characteristics, flux calibration and flat-fielding artifacts.
