1/6 + 1/12 + 1/20 + ... + 1/9900
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1/6+1/12+1/20+⋯+1/9900
=1/2⋅3+1/3⋅4+1/4⋅5++⋯+199⋅100
=(1−12)+(12−13)+(13−14)+(14−15)+(15−16)+⋯+(199−1100)
=1−1100
=99/100
Explanation:
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