Math  /  Calculus

QuestionDetermine if each infinite geometric series diverges or converges. If the series converges, type the sum. If the series diverges, type: diverges 1) i=1(3(14)i1)\sum_{i=1}^{\infty}\left(3 \cdot\left(\frac{1}{4}\right)^{i-1}\right) \square Check Show answer 2) i=1(23i1)\sum_{i=1}^{\infty}\left(-2 \cdot 3^{i-1}\right) \square Check Show answer 3) i=1(41i1)\sum_{i=1}^{\infty}\left(4 \cdot 1^{i-1}\right)
Check Show answer 4) i=1(10(14)i1)\sum_{i=1}^{\infty}\left(-10 \cdot\left(-\frac{1}{4}\right)^{i-1}\right)

Studdy Solution
Calculate the sum of the fourth series:
S=a1r=101(14)=101+14=1054=8 S = \frac{a}{1 - r} = \frac{-10}{1 - \left(-\frac{1}{4}\right)} = \frac{-10}{1 + \frac{1}{4}} = \frac{-10}{\frac{5}{4}} = -8
The results are: 1) Sum = 4 4 2) Diverges 3) Diverges 4) Sum = 8 -8

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