1. Temukan jumlah dari: [tex](1 - \frac{1}{2} ) + ( \frac{1}{3} - \frac{1}{2 {}^{2} } ) + ( \frac{1}{3 {}^{2} } - \frac{1}{2 {}^{3} } ) + ....[/tex]
Answer (4)
Because when you build things with real wood and tools, negative length has no physical meaning. There are still two square roots, but we ignore the one that's not useful.
There is only one answer for the length of the side of a square window when given the area because physical lengths must be positive, so we only consider the positive square root.
Every positive number indeed has two square roots, a positive and a negative root, because if you square either a positive or negative number, the result is a positive number. However, when finding the length of the side of a square from its area, we only consider the positive square root because a length can't be negative. This concept is rooted in geometry, where the length of a side of a physical object must be a positive measure. Thus, there is only 'one' answer for the length of a side of a square when given the area.
For example, if the area of a square window is 9 square feet, both 3 and -3 are square roots of 9. However, only '3 feet' is a feasible measurement for the side of the window, as it represents an actual length. In mathematical terms, we take the principal square root for length which is always positive.
Every positive number has two square roots, but only the positive one is relevant for physical dimensions like length. For example, the square root of 16 is both +4 and -4, but the side length of a square must be positive. Therefore, we ignore the negative root because it does not have a real-world meaning.
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Jawaban:Hasil dari [tex]\tt{}(1 - \frac{1}{2} ) + ( \frac{1}{3} - \frac{1}{2 {}^{2} } ) + ( \frac{1}{3 {}^{2} } - \frac{1}{2 {}^{3} } )[/tex] adalah [tex]\tt{}\frac{41}{72}.[/tex]Penjelasan dengan langkah-langkah:[tex]\tt{}(1 - \frac{1}{2} ) + ( \frac{1}{3} - \frac{1}{2 {}^{2} } ) + ( \frac{1}{3 {}^{2} } - \frac{1}{2 {}^{3} } )[/tex][tex]\tt{}\frac{1}{2} + ( \frac{1}{3} - \frac{1}{4} ) + ( \frac{1}{9} - \frac{1}{8} )[/tex][tex]\tt{} \frac{1}{2} +( \frac{1 \times 4}{3 \times 4} \times \frac{1 \times 3}{4 \times 3} )+ ( \frac{1 \times 8}{9 \times 8} + \frac{1 \times 9}{8 \times 9} )[/tex][tex]\tt{} \frac{1}{2} + ( \frac{4}{12} \times \frac{3}{12} ) + ( \frac{8}{72} - \frac{9}{72} )[/tex][tex]\tt{} \frac{1}{2} + \frac{1}{12} - \frac{1}{72} [/tex][tex]\tt{} \frac{1 \times 36}{2 \times 36} + \frac{1 \times 6}{12 \times 6} - \frac{1}{72} [/tex][tex]\tt{} \frac{36}{72} + \frac{6}{72} - \frac{1}{72} [/tex][tex]\tt{} \frac{36 + 6 - 1}{72} [/tex][tex]\tt{} \frac{41}{72} [/tex]
