By attaching the verb
続（つづ）ける 'to continue' to the
conjunctive form of another verb, we will be able to express that '(A) is continuing'. Let's have a look at a few examples of this structure.
サリーは暗（くら）くなるまで走（はし）り続（つづ）ける。
Sally will continue to run until it gets dark.
私（わたし）は漢字（かんじ）を覚（おぼ）えるまで、同（おな）じ漢字（かんじ）を書（か）き続（つづ）ける。
I will continue to write the same kanji until I memorize it.
There is a difference in nuance between connecting one verb to another verb through the
conjunctive form, or through the use of the
conjunction particle て. The former implies that '(A) is being done in the way of (B)', while the latter implies that '(A) is being done, and then (B)'.
日本語（にほんご）は難（むずか）しいけど、勉強（べんきょう）を頑張（がんば）って続（つづ）ける。
Japanese is difficult, but I will give it my best and continue with study. (Emphasis on the continuation of studying)
日本語（にほんご）は難（むずか）しいけど、勉強（べんきょう）を頑張（がんば）り続（つづ）ける。
Japanese is difficult, but I will continue giving it my best with study. (Emphasis on the continuation of giving it one's best)