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數學知識交流-Compair

發問:

1) Which is bigger ? A.1222...2223(102 units) * 2333...3334(102 units) B.4555...5556(102 units) * 676767...676(101 units) 2) Which is smaller ? A.1/2+1/3+1/4+1/5+...+1/98+1/99+1/100 B.1/101+1/102+1/103+...+1/99999+1/100000 更新: Compare

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最佳解答:

1)A = 1222...2223 x 2333...3334 4550...0000 x 6760...000 = (455 x 67.6) x (10^198) = 30758 x (10^198)故 A line 1 + (1/1,101 + ... + 1/2100) .......line 2'' > line 2 + (1/2,101 + ... + 1/3100) ..........line 3'' > line 3 + ....... + (1/98,001 + ... + 1/99000) ...........line 99'' > line 99 + (1/99,001 + ... + 1/100000) ...........line 100Therefore A line 99 + (1/99,101 + ... + 1/100,00) ...........line 100 Therefore A
其他解答:

1) Which is bigger ? B.4555...5556(102 units) * 676767...676(101 units) 2) Which is smaller ? B.1/101+1/102+1/103+...+1/99999+1/100000|||||For #1.) Since 12*23