Exam Question : Usage of Binomial Formula

Harry - a vivd reader of askalwayslovely.blogspot.com sent me an email asking about solving of the following question. He did it using trial and error. I believe it will take him some time. He felt that his approach was not the best so he emailed me asking for alternatives.

In fact for this question, there is a step by step way which will get us the answer in less than 8 minutes time.

Question: If the coefficient of [pmath]x^k[/pmath] and [pmath]x^(k+1)[/pmath] in the expansion of [pmath](2x+3)^19[/pmath] are equal, find [pmath]k[/pmath]

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