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Because 25! = 25*(24!), and 25 itself is 100/4. So 25! = 10*(10/4)*24! Now since we are given 24! ~10^24, it follows that 25! ~ (10/4)*10^25. But 10/4 is just a
by IIAOPSW 3y ago
Because 25! = 25*(24!), and 25 itself is 100/4. So 25! = 10*(10/4)*24! Now since we are given 24! ~10^24, it follows that 25! ~ (10/4)*10^25. But 10/4 is just a bit over 2, not a strong enough multiplicative factor to break the "approximately equals relationship". Therefore 25! ~ 10^25.
QED