The sum of the series `(.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101)

Monjur Alahi

The sum of the series
`(.^(101)C_(1))/(.^(101)C_(0)) + (2..^(101)C_(2))/(.^(101)C_(1)) + (3..^(101)C_(3))/(.^(101)C_(2)) + "….." + (101..^(101)C_(101))/(.^(101)C_(100))` is `"____"`.


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Salim Ahmed Kawsar

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Correct Answer - 5151
Here `T_(r) = (r^(.1001)C_(r))/(.^(100)C_(r-1))= (r.(1001-r+1))/(r) = 102 -r`
`:.` Given sum `= underset(r=1)overset(101)sum(102-r)`
`= 101+100+99+"...."+2+1`
`=5151`

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