Partial Sums of Infinite Series
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Key Questions

A partial sum
#S_n# of an infinite series#sum_{i=1}^{infty}a_i# is the sum of the first n terms, that is,
#S_n=a_1+a_2+a_3+cdots+a_n=sum_{i=1}^na_i# . 
Answer:
#sum_1^(n=4)(3/2)^n = 12.1875# Explanation:
This is geometric progression series of which
first term is
# a=3/2=1.5# , common ratio is#r=1.5# #4 # th partial sum ; i.e#n=4# Sum
# S= a * (r^n1)/(r1)= 1.5 * ((1.5^41)/(1.51))=12.1875# #sum_1^(n=4)(3/2)^n = 12.1875# [Ans]
Questions
Tests of Convergence / Divergence

1Geometric Series

2Nth Term Test for Divergence of an Infinite Series

3Direct Comparison Test for Convergence of an Infinite Series

4Ratio Test for Convergence of an Infinite Series

5Integral Test for Convergence of an Infinite Series

6Limit Comparison Test for Convergence of an Infinite Series

7Alternating Series Test (Leibniz's Theorem) for Convergence of an Infinite Series

8Infinite Sequences

9Root Test for for Convergence of an Infinite Series

10Infinite Series

11Strategies to Test an Infinite Series for Convergence

12Harmonic Series

13Indeterminate Forms and de L'hospital's Rule

14Partial Sums of Infinite Series