Theorem 2: Series of Sums is equal to Sum of Series

In this video, I go over Theorem 2, which states that we can move a constant out of the sum of a series as well as add or subtract series individually. These follow from the Limit Laws of Sequences, and I use this to prove that the series involving an addition of terms is equal to an addition of the individual series. I go over an example, as well as make a note that a finite number of terms does not affect the convergence or divergence of a series. #math #calculus #series #sequences #education Timestamps: Theorem 2: Adding and subtracting convergent series – 0:00 Proof of part ii of Theorem 2 via Limit Laws for Sequences – 1:54 Taking the limit as the sum of partial sums approaches infinity – 3:55 The series of sums is equal to the sum of the series – 6:23 Example 9: Series of sums – 7:39 Solution: The second series is a convergent geometric series that sums to 1 – 8:03 The first series was solved from Example 6 via the telescoping sum and is equal to 3 – 9:42 Adding the series obtains 3 + 1 = 4 as the sum – 11:00 Note 4: A finite number of terms doesn't affect the convergence or divergence of a series – 11:40 Notes and playlists: Hive: https://3speak.tv/watch?v=mes/theorem... Notes: https://peakd.com/mathematics/@mes/la... Playlist:    • Infinite Series: Definition, Examples, Geo...   Sequences and Series:    • Infinite Sequences and Series   MES Links: https://mes.fm/links . ------------------------------------------------------ Become a MES Super Fan!    / @mes   DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps