Question

the sum of the series 25/72+25/90+25/110+25/132+-----+25/9900

Answer 1

The sum of the series is 2.875

• A series in mathematics is essentially a description of the process of successively adding an infinite number of quantities to a specified initial quantity. A significant component of calculus and its generalisation, mathematical analysis, is the study of series. Most branches of mathematics use series, including combinatorics, where generating functions are used to explore finite structures. In addition to being widely utilised in mathematics, infinite series are also used extensively in physics, computer science, statistics, and finance, among other quantitative fields.
• For a very long time, it was thought absurd that such a potentially infinite summation could yield a finite result. During the 17th century, this conundrum was answered utilising the idea of a limit. This illogical characteristic of infinite sums is illustrated by Zeno's paradox with Achilles and the tortoise: Achilles chases a tortoise, but by the time he catches up to it in its starting place, the tortoise has moved on to a new spot; when he reaches this new spot, the tortoise has moved on to a new spot, and so on.

Here, according to the given information, the series is given as,

$\frac{25}{72}+\frac{25}{90}+\frac{25}{110}+\frac{25}{132}+...+\frac{25}{9900} \\=25((\frac{1}{8}-\frac{1}{9})+ (\frac{1}{9}-\frac{1}{10})+...+(\frac{1}{99}-\frac{1}{100}))\\=25((\frac{1}{8}-\frac{1}{100})\\=2.875$

Hence, the sum of the series is 2.875

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