Use the formula for the binomial series: m(m-1) m(m-1).(m-k+1), (1 + x)" 1+ mx + x² + 2! ... ... k! 1+ 2k=1 m(m-1)..(m-k+1) x if |지 < 1 k! to obtain the Maclaurin series for V1 + x. 1 1 + r+ E(-1)*+16· 13 · 20--(7k – 8) k! k=2 1+ E(-113 · 20(7k – 8) 7kk! k=1 r + E(-1)*+16 · 13 · 20-(7k – 8) 7k k! 00 1+r+ > k=2 00 1 6. 13 · 20..(7k – 8) 7* k! k=2 13 · 20..(7k – 8) 1+ 2: k! k=1

Q: Find the sum of the series n (r +1) (n+2)* 32 (n +3*) 3/2 as n → 00_ n +(n-1)| 3/2

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Q: What is the sum of the infinite series 4 2n 37 ()* 37 2 2 1 +...+ (-1)" + (2n+1)! •• ? 3! 5! 7! O -1…

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Q: Which series given below converge conditionally. (-1)" n=2 n²+1 (-1)" 2 Inn 1) E-2 00 II) E, (-1)"…

A: For details solution see the  answer below

Q: Find the Maclaurin series 15 of I 8 1+X

A: From the formula for maclaurin series we solve the given problem

Q: Find the sums of the series

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Q: Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k!…

A: 1 + xm = 1+ mx + ∑k - 2∞m(m - 1)(m - 2) ... (m - k + 1)k!xk if x &lt;1 is the binomial expansion. We…

Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: Find the Maclaurin series for the given function. SELECT A) B) sin(10z) (-1)*102m+1,an (2n + 1)! 8…

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Q: c) Show that the series Em+2 diverges.

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Q: Find the limit of the series 3-1 + 3-2 + 3-3 + ...+ 3-n+ ... additionally, write the sum in sigma…

A: Given: series is 3-1+3-2+3-3+…+3-n+… To be find: limit of the series and write sum in sigma…

Q: Use the formula for the binomial series: (1 + x)" = m(m-1)2 + ... + 2! m(m–1).-(m-k+l) ,k + k! 1 +…

A: Given function is 1(1 + x)6

Q: Use the formula for the binomial series: (1 + x)" 1+ mx + m(m-1)2 + m(m–1)--(m–-k+1), + + ... k!…

A: We need to find Maclaurin series for , 11 + x3. We have given that ,  1 + xm = 1 + mx + m(m-1)2!x2 +…

Q: Find the first four terms of the Legendre series of [0 if-1<x<0 x if 0<x< 1 f(x) =

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Q: What is the seventh term in the Taylor series for 4+1 about the base point 1? Ox7 07 O (2-1) .7! 00…

A: I have used the taylor series expansion to solve this

Q: verify that the series diverges

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the exact sum of the series…

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Q: Find the Maclaurin series for the given function. A) B) 6+z (-1)"z*+1 6 (-1)"z" o 6+1 D) (-1)"z"…

A: In this question we have to find the Maclaurin series of the function.

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

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Q: Evaluate the telescoping series or state whether the series diverges. (If the quantity diverges,…

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Q: determine the convergence or divergence of the series

A: Step 1:Step 2:

Q: (a) Give an instance of the Binomial Series which begins as follows: 10 1 - 6z² +24z¹ - 80z6 +240z8…

A: Given binomial series Note: According to the guidelines we are allowed to solve one question at 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…

Q: The sum of the series (-1)" (37)2n+1 - is 22n+1 (2n + 1)! n=1

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