1/2 + 1/6 + 1/12 + ... + 1/9900 + 1/10100
= 1/1.2 + 1/2.3 + 1/3.4 +... +1/99.100 + 1/100.101
= 1/1 - 1/2 + 1/2 + 1/3 - 1/3 + 1/4 +... + 1/99 - 1 / 100 + 1/100 - 1/101
= 1/1 - 1/101
= 100 /101
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