& use series representation to dippprovimate the integral (Hint ! Sum the fiirst four terms of the series

Q: 3 5) Find a power series for X +

A: Let  f(x) = 3/(x+5)

Q: Find the sum of the series. 5(-1)^²n +1 Σ 62n + 1(2n + 1)! n = 0 62n +

A: The sum is evaluated below.

Q: e method fo determine Use any whether the Series Conve 2. (K +1)! K= 1 6.

A:

Q: Express as the sum of a power series: (5z + 6)(6z + 6) (3)"] 1/7 17

A: Using partial fractions:  x5x+66x+6=15x+6-16x+6                            =1/61--56x-1/61--x…

Q: Find the sum of n terms of the series 1.24 +2.3 +3.4 +..

A:

Q: What is the center of the power series

A: We have to find the centre of the given power series.

Q: Write the first five terms (or the series in summation notation) of the Taylor series for ex-3

A: We have to find first five terms (or the series in summation notation) of the Taylor series for ex-3

Q: Question 8 Find the sum of the series Σπο 32n+(-2) 10"

A:

Q: Find the first four terms of the binomial series for the function shown below. (1-x) -1/5 The first…

A: Use the formula of the Binomial Theorem to solve this problem.

Q: A +a Cos x the series is 1/-

A: Using ratio test,

Q: Write the first five terms (or the series in summation notation) of the Taylor series for 2x2 /…

A:

Q: Write a Taylor series for In(4 + 2x) centered around x-0. Please write the series in summation…

A: Taylor series

Q: Find 81 term of series 41,43,45...

A: As we know that; The expression for the nth term of the arithmetic sequence is: Tn=a+n-1d Where, a…

Q: b) (-1) (1) d) nn 맛 UMU 1 n)

A:

Q: The binomial series of the form i+3x be written as

A: Binomial Expansion: The binomial expansion for (1+x)n is given by, The given function can be…