If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it. - Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Chukwuemeka

Questions on Series

Samuel Dominic Chukwuemeka (SamDom For Peace)

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(1.) Determine the sums of these infinite series.

$ (a.)\;\; \sum\limits_{n = 1}^\infty \dfrac{7}{2^n} \\[5ex] (b.)\;\; \sum\limits_{n = 1}^\infty \left(\dfrac{1}{2^n} - \dfrac{1}{2^{n + 1}}\right) \\[5ex] (c.)\;\; \sum\limits_{n = 1}^\infty \left(\dfrac{1}{2^n} - \dfrac{1}{2^{n - 1}}\right) \\[5ex] $

$ $
(2.) For the series: $\sum\limits_{n = 1}^\infty \left(-\dfrac{3}{5}\right)^{n - 1}$

(a.) Identify the type of series.
(b.) Determine whether it converges or diverges.
(c.) If it converges, calculate the sum.


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