Series Convergence/Divergence

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                Checking convergence of series

Let {a_{n} } be the sequence of real numbers .

The expression    a_{1}+a_{2}+a_{3}+......+a_{n}    is called finite series  and is denoted  using sigma notation as

\mathbf{\sum_{i=1}^{n}a_{i}}

The expression   a_{1}+a_{2}+a_{3}+......+a_{n}+......   is called  infinite series  and is denoted  using sigma notation as

\mathbf{\sum_{i=1}^{\infty }a_{i}}

A series  either converge or diverge and there are many tests to check convergence of different type of series.

Here we are going to study them one by one.

 

Relations and functions

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Applications of Integral calculus

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Integral Calculus

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Integral calculus

The process of finding an indefinite integral of a given function is called integration of function. This is denoted by ∫f(x) dx and read as indefinite integral  of f(x) with respect to x.

Here, ⎰ is called integral sign, f(x) is the integrand, x is the variable of integration and dx is the element of element of integration.

Integral is also called antiderivative as this is just the reverse of derivative.

\dpi{120} \mathbf{\frac{d}{dx}\left ( \int f(x)dx \right )= f(x)}

Differentiation of an integral is the integrand itself .

Differentiation and integration  are inverse operations.

Integral calculus has numerous applications  like it is used in finding area under the curve, finding volume of solids, finding arc lengths, finding surface of revolution, work done by force and many more.

Applications of Differential Calculus

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