¿Puedes calcular el numero de esferas que hay en la figura 15? | Razonamiento inductivo

Academia Internet

20 Sept 201907:38

Summary

TLDRIn this video, viewers are introduced to inductive reasoning for solving logical-mathematical problems. The presenter explains how to identify patterns in triangular figures with spheres, progressively adding spheres per side. By using inductive reasoning, the number of spheres in each figure is determined through sums of consecutive numbers. The video demonstrates how to calculate the total number of spheres for different figures, such as 15 or 20, using a formula for triangular numbers. The approach emphasizes logical thinking and offers practical tips for solving complex problems.

Takeaways

😀 Inductive reasoning involves starting with specific cases and generalizing to a broader rule.
😀 In the problem, the task is to determine the number of spheres in triangular arrangements, like in figures 1, 2, 3, and 4.
😀 The number of spheres in each figure can be understood as the sum of consecutive integers (e.g., 1 + 2 + 3 for figure 3).
😀 The general formula for the sum of the first n consecutive numbers is: S = n(n + 1)/2.
😀 Using the sum formula, the number of spheres in figure 15 is calculated as 120 using the formula for triangular numbers.
😀 Triangular numbers refer to sums of consecutive integers that create a triangular arrangement, with each figure forming a progressively larger triangle.
😀 For example, in figure 2, there are 3 spheres (1 + 2), and in figure 3, there are 6 spheres (1 + 2 + 3).
😀 A quicker way to compute the number of spheres is to use the formula for consecutive sums, allowing for faster results.
😀 The formula for the nth triangular number can be applied directly, avoiding the need to manually sum large numbers of spheres.
😀 The instructor also demonstrates an alternate method for finding the number of spheres by multiplying the figure number by 2 and adding 1 (e.g., 20 × 2 + 1 = 41 for figure 20).

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