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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[...] to use the Binomial formula provided on the formula sheet? (term by term expansion, (r+1)th general term, factorial [...]