Superheroes fighting with maths

Calculus Level 2

Electro and Spider-Man ( Spidey! ) are going to fight! This being a maths problem,we'll skip the specifics of this but we do know that both Electro and Spider-Man have a health of \( 500 \) units.Also, Electro can take away \( 50 \) units of health per second with his electro-powers.That means Spider-Man will have to defeat Electro in 10 seconds! Luckily, Spider-Man is extremely fast and he can strike Electro \( \infty \) times ( I know it's not possible, but this is calculus ) in 10 seconds but he will lose \( \frac{9}{10} \) of his striking power every time ( in other words, every attack is \( \frac{1}{10} \) as strong as the last and takes away only \( \frac{1}{10} \) as many units of health ).What is the minimum initial striking power Spider-Man must have ( in units of health ) to be able to defeat Electro?

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