P-SERIES TEST FOR CONVERGENCE AND DIVERGENCE

For each of the following infinite series, determine whether it converges or diverges.

Problem 1 :

Solution :

Since p = 4 > 1, the given series converges.

Problem 2 :

Solution :

Since p = ⅔ = 0.666..... < 1, the given series diverges.

Problem 3 :

Solution :

Since p = ⁵⁄₄ = 1.25 > 1, the given series converges.

Problem 4 :

Solution :

Since p = ⅕ = 0.2 < 1, the given series diverges.

Problem 5 :

Solution :

Since p = ³⁄₂ = 1.5 > 1, the given series converges.

Problem 6 :

Solution :

Since p = ⅔ = 0.666..... < 1, the given series diverges.

Problem 7 :

Solution :

Since p = ½ = 0.5 < 1, the given series diverges.

Problem 8 :

Solution :

Since p = -½ = -0.5 < 1, the given series diverges.

Problem 9 :

Solution :

Since p = π - e < 1, the given series diverges.

Problem 10 :

Solution :

Since p = 2e - π > 1, the given series converges.

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