If humans have 23 pairs of chromosomes and apes have 24 pairs of chromosomes, then there must have been a time during our evolutionary history when 2 chromosomes fused to form just 1. My question is that if one member of this species randomly mutated to have 1 less pair of chromosomes than all the other individuals in its species, then all the other members of that species would still have 24 pairs. Therefore, any offspring born to the new mutated individual would be infertile, so the mutation would never be passed on. How would this adaptation to our species happen?
There is actually very good evidence that human chromosome 2 resulted from a fusion of two ape chromosomes, 2p and 2q. Each chromosome has distinct sequences at both ends called telomeres, as well as a unique central region called a centromere. If two ape chromosomes fused end to end (a phenomenon known as a Robertsonian translocation), we would expect to see two indicators of this translocation in the human chromosome. First, the fused chromosome should have two centromeres. Second, traces of telomeres should be evident in the middle of the chromosome where the fusion occurred. In fact, both of these predictions are supported. The normal centromere on human chromosome 2 corresponds with the centromere on chimpanzee chromosome 2p, while traces of a second centromere are observed in the region of the human chromosome that lines up with the centromere of chimp chromosome 2q. Also, the repetitive DNA sequences characteristic of telomeres are found precisely at the predicted fusion site, and the repeats reverse direction exactly as would be expected for two chromosomes joined end to end.
Despite having a different number of chromosomes, an individual carrying a Robertsonian translocation has not lost any genetic material and can therefore mate with a normal individual and produce viable, fertile offspring. A useful diagram (learn.genetics.utah.edu/units/disorders/karyotype/robertsonian.cfm) shows the possible chromosome combinations that can result from this pairing. One-fourth of the offspring would receive the standard combination of chromosomes and would of course be normal and would not be able to pass on the fused chromosome to future generations. Half the offspring would receive either only one copy or three copies of one chromosome; these individuals would be unlikely to survive or reproduce successfully. The remaining one-fourth of the offspring would inherit a balanced Robertsonian translocation. These individuals would also be viable and fertile and could found a lineage carrying only the fused chromosome if they mated amongst themselves.
A well-known example of this situation can be found in the Przewalski's wild horse, formerly extinct in the wild but recently reintroduced into its native habitat in Mongolia. This horse is closely related to the domesticated horse, but it has 33 pairs of chromosomes whereas the domesticated horse has only 32 due to a translocation. However, if the two are crossed, they can produce fertile offspring.
For further reading:
This website has a diagram showing how chromosomes from human, chimpanzee, gorilla, and orangutan align with each other. Note the fusion of ape chromosomes in human chromosome 2.
This website discusses the genetic consequences of Robertsonian translocations.