とうとう

The word とうとう can be used to express that an expected situation has occurred after an extended period of time. It's similar to ついに, although とうとう is less formal. It can be translated as "eventually", "in the end", "after all", or other similar meanings.

彼は、その数学の問題を何時間も考えたが、答えが分からなかったので、とうとうあきらめてしまった。
He thought about the math problem for hours, but in the end he gave up because he didn't understand the answer.

リーさんは毎日四時間に勉強して、とうとう合格出来たんだ。
Lee-san studied for four hours every day, and in the end he was able to pass the test.

１５年も飼っていた犬が、年を取ってとうとう死んでしまったので、とても悲しい。
I'm really sad, because the dog that I'd had for 15 years grew old and finally died.

大学のサッカーのチームに入りたかったけど、とうとう落とされてしまった。
I wanted to join the university soccer team, but I was rejected after all.