Hi Math guys. I have a few problems. I need you to tell me if they are convergent or divergent
1. Is the series 2 + 3 + 4 + 5+... convergent or divergent?
2. Is the series 2 + 10 + 50+... convergent or divergent?
3. Is the series 1/4 - 1/16 + 1/64+ ...convergent or divergent?
1. Is the series 2 + 3 + 4 + 5+... convergent or divergent?
2. Is the series 2 + 10 + 50+... convergent or divergent?
3. Is the series 1/4 - 1/16 + 1/64+ ...convergent or divergent?
-
For a series to converge limit n --> ∞ Un = 0
1. 2 + 3 + 4 + 5 + .... + n
Thus, Un is n. Hence, limit n ->∞ of n = ∞ diverges
2. 2 + 10 + 50 + ..... + 5^n
Thus, Un is 5^n. Hence, limit n ->∞ of 5^n = ∞ diverges
3. 1/4 - 1/16 + 1/64 + .... + (1/4) * (-1/4)^(n-1)
Thus, Un is (1/4) * (-1/4)^(n-1). Hence, limit n ->∞ of (1/4) * (-1/4)^(n-1) = (1/4) * 1/∞ = 0 converges
1. 2 + 3 + 4 + 5 + .... + n
Thus, Un is n. Hence, limit n ->∞ of n = ∞ diverges
2. 2 + 10 + 50 + ..... + 5^n
Thus, Un is 5^n. Hence, limit n ->∞ of 5^n = ∞ diverges
3. 1/4 - 1/16 + 1/64 + .... + (1/4) * (-1/4)^(n-1)
Thus, Un is (1/4) * (-1/4)^(n-1). Hence, limit n ->∞ of (1/4) * (-1/4)^(n-1) = (1/4) * 1/∞ = 0 converges
-
1. divergent
2. divergent
3. convergent
2. divergent
3. convergent