You should fill in the words! First you shade in half the area. Then you shade in half of the remaining 1/2 half, ie you shade in 1/4 of the area leaving 1/4 of the area still unshaded. Of the 1/4 of the remaining area you shade in 1/2 of that area leaving the other half (1/8 of the area) unshaded. ....Okay, thanks a lot!
I'd suggest getting a good command of "classical" proofs before searching for more exotic ones. In the case of this series you can try a different approach: 1) prove that the sum is limited from above; then the fact that it is monotonic means it must converge; then apply post #14. But "geometric proofs" rarely qualify as formal ones.Yes, but I want to learn different kinds of proofs than using the definition.
I will take a stab at it.You should fill in the words! First you shade in half the area. Then you shade in half of the remaining 1/2 half, ie you shade in 1/4 of the area leaving 1/4 of the area still unshaded. Of the 1/4 of the remaining area you shade in 1/2 of that area leaving the other half (1/8 of the area) unshaded. ....