Question

find value of 1/2+1/3+1/6........10th terms​

Answer 1

Sum of the series is $\frac{-5}{2}$.

• 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.

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

$\frac{1}{2} +\frac{1}{3} +\frac{1}{6} +...$

We need to find the sum of the series upto 10 terms.

Now, the series is in arithmetic progression.

The common difference is,

$\frac{1}{3} -\frac{1}{2}= -\frac{1}{6}$.

Now, the first term of the series is, $\frac{1}{2}$ and the number of term is 10.

Then, we get,

Sum of the series = $\frac{n}{2} (2a+(n-1)d)$

This gives,

Sum of the series =

$\frac{10}{2} (1+(10-1).\frac{-1}{6} )\\=5(1-\frac{3}{2} )\\=-\frac{5}{2}$

Hence, sum of the series is $\frac{-5}{2}$.

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