Question

efectuati:(10 000-1 la puterea 2)x (10 000- 2 la puterea 2) x (10 000 - 3 la puterea 2)x...x(10 000 - 98 la puterea2)

Answer 1

10000=100²
10000-1²=100²-1²=(100-1)(100+1)=99·101
10000-2²=100²-2²=(100-2)(100+2)=98·102
10000-3²=100²-3²=(100-3)(100+3)=97·103
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10000-97²=100²-97²=(100-97)(100+97)=3·197
10000-98²=100²-98²=(100-98)(100+98)=2·198
Daca facem produsul acestor numere, obtinem:
2·3·4·.....·99·100/100·101·102·.........·197·198=198!/100

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