In my previous post(Heuristic-math-problem-solving-skill), I asked the readers to find the sum of the first $n$ terms for the series:
$1+2(1-x)+3(1-x)(1-2x)+4(1-x)(1-2x)(1-3x)+\cdots+n(1-x)(1-2x)\cdots(1-(n-1)x)$
This is one really hard math Olympiad contest problem, but fortunately logical thinking and heuristic problem solving skills are something that we can teach.
Showing posts with label heuristic problem solving skills. Show all posts
Showing posts with label heuristic problem solving skills. Show all posts
Evaluate √((1000000)(1000001)(1000002)(1000003)+1)
Evaluate $\sqrt{(1000000)(1000001)(1000002)(1000003)+1}$ without the help of calculator.
At first glance, you might notice $1000000,\,1000001,\,1000002,\,1000003$ are the terms from arithmetic sequence and now, we have to compute the product of these four figures, but not to find the sum of the first four terms from that sequence.
But, let us look at it a lot more closely, we can actually now discern a pattern if we employ the heuristic strategy by using the substitution method which helps in solving this intriguing problem.
At first glance, you might notice $1000000,\,1000001,\,1000002,\,1000003$ are the terms from arithmetic sequence and now, we have to compute the product of these four figures, but not to find the sum of the first four terms from that sequence.
But, let us look at it a lot more closely, we can actually now discern a pattern if we employ the heuristic strategy by using the substitution method which helps in solving this intriguing problem.
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