Question

derive an expression for infinity

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Answer 1

Answer:

Infinite Geometric Series Formula Derivation

We know that the formula for computing a geometric series is:∞∑i=1a0ri−1=a01−r.

Method 1 (The way I found on my own): ∞∑i=1a0ri−1≡S.

Method 2 (The way I found on the web): n∑i=1a0ri−1≡Sn.

Method 1 for formula of partial sums: n∑i=1a0ri−1≡Sn.

Answer 2

$step \: by \: step \: explanation$

*Identify a1 and r.

*Confirm that − 1 < r < 1 \displaystyle -1<r<1 −1<r<1.

*Substitute values for a1 and r into the formula, S = a 1 1 − r \displaystyle S=\frac{{a}_{1}}{1-r} S=1−ra1.

*Simplify to find S.

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