This will be my first guide and an introduction to a new kind of champion:
The MDC (Mixed Damage Carry) - bruiser.
Though I'm not a very skilled player, I know that this build/guide will help to fully master "W"- Hyper Charge!

The good stuff:
+ High damage burst.
+ Good initiation/running with his E.
+ Slow and knockback in his hammer form.
+ Lots of movement speed with his passive and E.
+ Fast farmer.
+ Free MR and armour with his hammer.
+ Insane burst with his W+SoD+BotRk (I'll get to that later)

The bad stuff:
+ Can easily be countered with CC, such as a silence.
+ Pretty squishy without runes.
+ Needs to farm a lot.
+ Won't do so much damage with abilities on lower lvl than 3.
+ Mana hungry.
+ Not so secret skillshot if W is placed.

For runes I recommend defensive on yellows and blues and offensive on reds and quints.

Reds:Flat AD. A must-have for Jayce in order to deal enough
dmg during the first three lvls.
Yellows:Flat armour or armour per lvl. When switching to cannon
you'll lose some of your armour, so be sure to get theeses runes.
Blues:Flat MR or MR per lvl. He also loses some MR when switching to
cannon.
Quints:Attack speed or Critical damage. You can choose between getting
the DPS or the Crit DMG.

DPS will help you to get your mana back with your W-passive.
Crit DMG will help you to deal more damage with
your Sword of the Divine.

Yes, it's very important for those who want to play MDC to max Jayce's second ability, Lightning Field/ Hyper Charge.
Put point on ult, Mercury Hammer/ Mercury Cannon at Lvl 6,11 and 16.
Max either his third ability, Thundering Blow/ Acceleration Gate or his first
ability, To The Skies!/ Shock Blast after maxing his W. The choice is yours!

This chapter is just a small guide about what's so good with the Sword of the Divine.

*Sod grants attack speed and crit on three basics.
*Getting a kill reduces the cool down on the active by 50%.
*Getting 2 kills reduces the cool down on the active by 100%, which means you can activate it
twice during a team fight.
*Basics get cool sound when activated.
*basics get cool FX when activated.
*can be used to almost kill an opponent under 10 sec.

Starters:

Start the game with Boots and 3 pots.
Either 2 Health Potion and 1 blue Mana Potion or 3 red Health Potion.

Core:

Rush for the Sword of the Divine and after that a The Brutalizer.
Sword of the Divine? Yes, together with your W- Hyper Charge, you'll
crush your foes with ease.

After that, buy a Blade of the Ruined King and upgrade your brutalizer into a
Black Cleaver.
When Ruined king got some attack speed it became one of the best
"tank-destroyer weapons" in LoL.
Together with your "W+SoD combo" you'll literally eat your enemies HP. It also have this nice active which let you drain some HP from your enemies.

The last items:

Going well?
Buy Frozen Mallet for the passive and HP and finish your build with either
Guardian Angel or Maw of Malmortius.
When to buy Maw: When there isn't any big threats in the enemy team.
When to buy Angel: When there is a chance to get killed during team fights or in a 1v1.

Going bad?
Buy Randuin's Omen to save yourself from the enemy carry (probably the biggest threat to you)
and slow any enemies hunting you or your allies. Buy either Spirit Visage
or Runic Bulwark as your last item.
When to buy Visage: When there's still a chance to turn the game, or when magic DMG is the
biggest problem to you during battles.
When to buy Bulwark: When you can handle yourself but your allies need more defensive stats.
Also grants your allies a little more HP-regen.

Now I'll explain the reason for playing Jayce like this:

THE AMAZING " Hyper Charge + Sword of the Divine + Blade of the Ruined King" COMBO.
(for short- "W+SoD+BotRK"-combo or "Mixed DMG carrying")

this is what you'll get:
1. Hyper Charge (Lvl.5) - 130% of your AD as DMG for three shots.
2. Blade of the Ruined King - 5% of your targets current HP as bonus magic-DMG to your basics.
3. Sword of the Divine - Making these three shots to crit, dealing twice as much DMG.
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Some math for those who care:

Let's say that you are facing a Garen at top lane.
Now let's say that both of you are about Lvl 16, that gives Jayce about 100 AD and Garen about 2000 HP. Note. you are the only one with items ( Sword of the Divine and Blade of the Ruined King) and no one has runes.

If you attack him with your "combo" you would deal
(MD=magic DMG, PD=physical DMG)

1# shot: 130 PD (thanks to your W) + 100 MD (5% of Garens current HP) x 2 (CRIT from SoD)
2# shot: 130 PD + 77 MD (5% of Garens current HP after your first shot) x 2 (CRIT again)
3# shot: 130 PD + 56 MD (5% of Garens remaining HP after your previous shots) x 2 (CRIT)

The damage your shots will deal against this Garen (total):

First shot: 460 Mixed Damage
Second shot: 414 Mixed Damage
Third shot: 372 Mixed Damage
total: 1246 Mixed Damage

After that, just finish him with your other skills.

NOTE. This is just an example of how the combo works, it won't always deal this much damage but
at least you know how to find out with this equation

Thanks for reading my first guide and I hope it will help you when playing against HP-tanks.
If you felt that some thing was missing or was needed to be said, please leave a comment.