Calculus Series review

Geometric and harmonic series

100

Determine whether the series converges or diverges Σ(5/6n)

What is Diverge,

200

Determine whether the following series converge or diverge Σ(-6)^(3-n)/8^(2-n)

What is Diverge,

300

Determine whether the series converges or diverges Σ(3^(2+n))*(2)^(1-3n)

What is convergent

400

Determine whether the series converges or diverges Σ (5^(n+1))/7^n-2

What is convergent

500

Determine whether the series converges or diverges Σ4^(n-1)/3^(n)

What is divergent,

Integral and P-Series

100

Determine whether the series converges or diverges 1/n^(1/3)

What is Diverge, 1/3 < 1

200

Determine whether series diverges or converges 2/n(n^(1/2))

What is Converge, 2/n(n^(1/2)), n x n^(1/2) = n^(3/2), 3/2>1,

300

Determine whether series diverges or converges n=0 Σ3n^2 *e^-3n

What is convergent, u = -n^3, du = -3n^2, lim as n approaches - infinity = 1

400

Determine whether series diverges or converges n=0 Σn^2 / (n^3)+ 1

What is diverges,

500

find that value of p that makes the series converge 1/(x*(lnx)^p

What is p>1, use integral test to find that series coverges when x >1, u = ln x, du = 1/x

Comparison Tests

100

Determine whether the series converges or diverges Σ1/((n^3+1)^(1/2))

What is converge, Use LCT to find that bn = 1/n, limit of series as n approaches infinity x 1/bn is positive and finite, 3/2 > 1

200

FREE BEE

300

Determine whether the series converges or diverges Σ(3n^2+5n^4)(n+1)^-5

What is Diverges, use LCT, bn = 1/n, lim is positive and finite , bn is harmonic series

400

Determine whether the series converges or diverges Σ1/n(n^2+1)^(1/2)

What is converge, bn = 1/ n^2, lim is positive and finite, use p-series for bn, 2>1,

500

Determine whether the series converges or diverges Σ1+sin(n)/n^2

What is converge, 1/n^2 + sin(n)/n^2, 1/n^2 converges by p-series, sin(n)/n^2 <= 1/n^2 therefore converges 

Alternating Series/ absolute convergent

100

Determine whether the series converges or diverges. if converges, determine absolutely or conditionally Σ(-1)^n/(2n+1)

What is converges conditionally 

200

Determine whether the series converges or diverges. if converges, determine absolutely or conditionally Σ((-1)^n) * ln(n)/n

What is converges conditionally,

300

Determine whether the series converges or diverges. Σ((-1)^(n+1))/7+2n

What is converges 

400

Determine whether the series converges or diverges. Σ((-1)^n )*e^-2n

What is converges 

500

Determine whether the series converges or diverges. Σ((-1)^n )/2^n

What is convergent

Ratio and Root

100

Determine whether the series converges or diverges Σn^7/7^n

What is converge, use ratio test, (n+1)^7/7^(n+1) x (7^n)/n^7 , lim (n+1)^7/7n^7 =1/7 <1

200

Determine whether the series converges or diverges Σ(3n!/5n+1)

What is diverges,

300

Determine whether the series converges or diverges Σ(e^4n)/(n-2)!

What is converges,

400

using the ratio test Determine whether the series converges or diverges. Σ((-1)^(n+1))/6n+7

What is inconclusive.

500

Determine whether the series converges or diverges. Σn^2/(2n-1)!

What is converges,