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By comparing areas, show that 1/2 + 1/3 + ... + 1/n

User TimVdG
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Final answer:

Comparing areas can demonstrate that the sum of fractions from 1/2 to 1/n is bounded and can be determined by finding common denominators. Understanding simple fractions like halves and thirds informs the process.

Step-by-step explanation:

Understanding the summation of fractions such as 1/2, 1/3, up to 1/n can be approached by comparing areas, much like the approach taken in conceptualizing common denominators.

For instance, if we know 1/2 of a half is one quarter, then similarly 1/2 of 1/3 must be 1/6, or in broader terms, combining fractions with a common denominator allows us to add their numerators directly, providing an easier way of calculating the sum.

Considering series expansions and the algebraic manipulation involved, we observe that adding a series of fractions from 1/2 to 1/n results in a sum that is bounded by known quantities.

User Ramesh Solanki
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