设函数，
当为正整数且时，证；
求

　　You never see him, but they're with you every time you fly. They record where you are going, how fast you're traveling and whether everything on your airplane is functioning normally. Their ability to withstand almost any disaster makes them seem like something out of a comic book. They’re known as the black box.
　　When planes fall from the sky, as a Yemeni airliner did on its way to Comoros Islands in the India ocean June 30, 2009, the black box is the best bet for identifying what went wrong. So when a French submarine (潜水艇) detected the device's homing signal five days later, the discovery marked a huge step toward determining the cause of a tragedy in which 152 passengers were killed.
　　In 1958, Australian scientist David Warren developed a flight-memory recorder that would track basic information like altitude and direction. That was the first mode for a black box, which became a requirement on all U.S. commercial flights by 1960. Early models often failed to withstand crashes, however, so in 1965 the device was completely redesigned and moved to the rear of the plane – the area least subject to impact – from its original position in the landing wells (起落架舱). The same year, the Federal Aviation Authority required that the boxes, which were never actually black, be painted orange or yellow to aid visibility.
　　Modern airplanes have two black boxes: a voice recorder, which tracks pilots' conversations, and a flight-data recorder, which monitors fuel levels, engine noises and other operating functions that help investigators reconstruct the aircraft's final moments. Placed in an insulated (隔绝的) case and surrounded by a quarter-inch-thick panels of stainless steel, the boxes can withstand massive force and temperatures up to 2,000℉. When submerged, they're also able to emit signals from depths of 20,000 ft. Experts believe the boxes from Air France Flight 447, which crashed near Brazil on June 1,2009, are in water nearly that deep, but statistics say they're still likely to turn up. In the approximately 20 deep-sea crashes over the past 30 years, only one plane's black boxes were never recovered.

   闻名于世的丝绸之路是一系列连接东西方的路线。丝绸之路延伸6,000多公里。得名于古代中国的丝绸贸易。丝绸之路上的贸易在中国、南亚、欧洲和中东文明发展中发挥了重要作用。正是通过丝绸之路，中国的造纸、火药、指南针、印刷等四大发明才被引介到世界各地。同样，中国的丝绸、茶叶和瓷器(porcelain)也传遍全球。物质文化的交流是双向的。欧洲也通过丝绸之路出口各种商品和植物，满足中国市场的需要。