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Question: Answered & Verified by Expert

Let 



a=n=1012002nk=101n1k! and b=n=1012002201-2nn! Then ab is


MathematicsSequences and SeriesKVPYKVPY 2020 (SB/SX)
Options:
  • A 1
  • B 32
  • C 2
  • D 52
Solution:
1013 Upvotes Verified Answer
The correct answer is: 1

a=n=1012002nk=101n1k!



=2101101!+21021101!+1102!+21031101!+1102!+1103!+



+22001101!+1102!++1200!



2101++2200101!+2102++2200102!++2200200!



=21012100-1101!+2102299-1102!++2200200!



=2201101!-2101101!+2201102!-2102102!++2201200!-2200200!



=n=1012002201-2nn!=b



ab=1


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