Group 1
sum_(n=1)^oo3(3/2)^n
Diverge by geometric 3/2>1
sum_(n=1)^oo(n/(2n+12))
Diverges by nth term Lim = 1/2 does not equal 0
sum_(n=0)^oo(-.9)^n
Converge by alternating series test OR geometric Test
sum_(n=0)^oo(2/n^(3/2))
p-series converges 3/2>1
sum_(n=1)^oo(7n^(-4))
p-series 4>1 converges
sum_(n=o)^oo(9/2^n)
Converge by geometric or ratio test
sum_(n=3)^oo(7^(n+2)/5^(2n))
Diverge by geometric r=7/25
sum_(n=1)^oo((-1)^(n+1)/(n!))
Converges by alternating series test
sum_(n=1)^oo(3^n/n^2)
Diverges by Ratio test
sum_(n=1)^oo(2/(n^2+5))
Converges by direct or limit comparison test
sum _(n=0)^oo(7-n+n^3)/(4n^3+6n+9)
Diverges by nth term
sum_(n=0)^oo((n^2)2^(n+1))/3^n
Converge by Ratio Test 2/3 <1
sum_(n=1)^oo((n+3)!)/((n+2)!)
Diverges by nth term test
sum_(n=1)^oo(n/((-2)^(n-1)))
Converges by the alternating series test OR Ratio test
sum_(n=1)^oo(n*e^(-n^2))
Converges by the integral test
sum_(n=1)^oo((n!)/10^n)
Diverges by the ratio test
sum_(n=1)^oo((lnn)^4)/n
Diverge by integral Test
sum _(n=1)^oo(2sin^2(n))/(n^5)
Converges by Direct Comparison Test (2/n^5)
sum_(n=2)^oo(n/((n^2+6))^4)
Converge by integral test or comparison Test (1/n^7)
For what values of p in the following series, would the series converge?
sum_(n=1)^oo(3/n^(p-3))
p>4 (must have exponent larger than 1 to converge by p-series)