40. (a) Starting with the geometric series Σπ–0 x", find the sum of the series Σ Σ n.xt-1 |x|<1 (b) Find the sum of each of the following series. (ii) Σ Σ (i) Σ nx", |x|<1 n-1 2"

Q: 2 3 (25-x2) 2

A: Given:The integral is,

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A: We will divide 55/5 first  Using long division 55/5=11

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A: To evaluate10a  - 17a + 3a

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A:

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A:

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A: Given query is to solve the equation.

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A: Given: 5-4c=c+20 for solving this we will use transportation

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A:

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A:

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A:

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A: Given,

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A: Given that

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A: Given information:The given expression is 8 + 4(8 - 2)2.

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A:

Q: (22-9)+(8+14)

A: The given expression is: (22-9)+(8+14)

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A: Simplify Taking x common

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A: Given expression is,

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A: The given expression is

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A: 8 + 7(42 - 3) = ?

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A: Assuming both the lines are parallel and line 1 passes through them. Then

Q: Find L 2 7 20] -4s+20

A: We will find the Laplace inverse transform.

Q: 3X C-6X)

A:

Q: (6z+3)+(5z+4)

A: 11z+7

Q: 1 0 4+9x2

A: we have to evaluate definite  integral as given