Amazon.com Inc. fell the most in three months after sales missed estimates, signaling that its investments in media services, Kindle devices and shipping promotions have been slow to pay off. Amazon shares dropped 7.7 percent to $179.46 after the Seattle-based company said yesterday that fourth-quarter revenue was $17.4 billion, trailing the $18.3 billion estimated by analysts in a Bloomberg survey. It was the biggest one-day stock decline since Oct. 26. Amazon, the world’s largest Internet retailer, got less revenue from digital media than anticipated, especially in the video-game market. The company also is relying more on third- party sellers, which can bolster profit but generate less revenue than direct sales.