b) Test the convergence of the series: 3 * 4 2 * 3+ 22√2 where * denotes usual multiplication. + 4 * 5 32√3 5*6 4²√4 + + ...8

Q: Determine whether the series is absolutely co Σ (-1)" + 1 n! n = 1

A: Given the series ∑n=1∞n65nn!(−1)n+1

Q: 5) Evaluate the following infinite series exactly. 10, 20. 40 а) 5+—+ 3 9 27 27 81 243 -+=+: 5! b)…

A: Please see the answer below.

Q: 3) Use the integral test to determine whether the following series is convergent or divergent. Σ n+6…

A:

Q: Which of the series α) x − x³ + x6 − x¹0 + x¹5 b) X x² x3 xs .... are power series?

A:

Q: How is the series 5 + 8 + 11 + ... +77 represented in summation notation? 25 ΟΣ(3q + 5) q=0 17 ΟΣ(4q…

A: Given Series is  5+8+11+........+77

Q: Limsup of the sequence is √√√n(√√n + 4. 1+ An = n Enter your answer here /n) n is a prime number n…

A:

Q: Find the sum of the series by recognizing how it is related to something familiar. 16z 21 A) e In(1+…

A: Expansion of e^x = 1+x+x^2/2! +x^3/3! and so on

Q: Inspired by Fibonacci, let us define a new series of numbers which we'll call the Conway numbers: f₁…

A: The new series defined as, f1=1f2=3fn=fn-1+fn-2, for n≥3. Thus we have the sequence 1, 3, 4, 7, 11,…

Q: Which of the series in are power series? a) 1 + x + (x − 1)² + (x − 2)³ + (x − 3)4 + ... b) x²+x+2

A: The general form of a power series is  and a power series has infinitely many terms.

Q: n3 A) Show that the series is converg ent b) Find minimum number of terms of the series that we need…

A: (a) Given that : ∑n=1∞-1nn.3n. Therefore, an=-1nn.3n Now, an+1=-1n+1n+13n+1=-1n.-13.n+1.3n…

Q: M8 Determine whether the series is absolutely covergent, condi hionelly conr or divergent 2 2n +)…

A: