calculus

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1. Calculus

   By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B)

2. Calculus

   Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as INF. If it diverges to negative infinity, state your answer as MINF. If it diverges

3. calculus

   determine if the series is absolutely convergent and convergent the sum from n=1 to infinity of sin(n^2)/n^2 what series test should I use and how? the ratio test?

4. Integral Calculus

   For what values of p is this series convergent? (summation from n = 1 to infinity) of ((-1)^(n-1))/(n^(p + 2)) A. p >= -2 B. p =/= -2 C. p > -2 D. for all p E. p > 0 You have to use the Alternating Series Test. I've already tried

1. Calculus

   Use the Integral test to determine whether the series is convergent or divergent. infinity "series symbol" n=1 (ne^(n"pi")) Note: I don't know how to solve or work out so show all your work. And give the answer in EXACT FORM

2. Calculus - Alternating Series Test

   Determine whether the infinite series, sigma(((-1)^(n+1))/n)^2 converges or diverges. My professor gave these in a problem set after he taught the alternating series test. Simplying the series we get, sigma(((-1)^(n+1))/n)^2

3. Calculus

   Determine whether the integral is divergent or convergent. If it is convergent, evaluate it and enter that value as your answer. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges

4. calculus

   Use the ratio test to determine whether the series is convergent or divergent. 1/2 + 2^2/2^2 + 3^2/2^3 + 4^2/2^4 + ...

1. Calculus - ratio test

   infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) |

2. Calc 2

   Determine whether the series is convergent or divergent series symbol n=1 to infinity (n^2/(e^(3n))

3. calculus

   Another problem: determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

4. Calculus

   Determine whether the series from 0 to infinity of cos(nπ)/(n + 3) converges conditionally or absolutely. A. The series diverges. B. The series converges conditionally but not absolutely. C. The series converges absolutely but

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