I'm not sure if this is worthy of the challenge section, but here goes.
Without using Taylor series/generating functions, show .
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The MacLaurin Series for for .
And finally .
Edit: Oops, didn't read the question fully stating not to use Taylor series hahaha. Ah well, it stays because it's beautiful
Here's another... .
Substitute so that . When and when and the integral becomes provided .
The rest should follow.
provided Isn't a Taylor series?
Hints (i) (ii) The following sequence is convergent (iii) Express (iv) Apply (i) to prove that
which is exactly the sum of the series. Fernando Revilla
Originally Posted by TheCoffeeMachine Isn't a Taylor series? No, it's a Geometric Series :P
Originally Posted by FernandoRevilla (ii) The following sequence is convergent (iii) Express You've got the right idea, but this step is not correct. Originally Posted by Prove It No, it's a Geometric Series :P It's also a Taylor series too!
Originally Posted by chiph588@ You've got the right idea, but this step is not correct. It is correct. Hint : Express Fernando Revilla
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