Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**almighty100****Member**- Registered: 2017-08-16
- Posts: 5

Consider the goemetric sequence:

which is valid for all

Taking the integral of both sides with respect to r, we have:

and if we let

note

for all natural numbers (so the restriction on is satisfied)

Therefore:

or more compactly:

for any natural number

So, for example,

*Last edited by almighty100 (2017-08-18 12:12:12)*

Offline

Thanks for the contribution! You will have a constant of integration lingering around, but this is easily dealt with by using the initial condition on your geometric series (or any suitable value of ).

**LearnMathsFree: Videos on various topics.New: Integration Problem | Adding FractionsPopular: Continued Fractions | Metric Spaces | Duality**

Offline