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The value of 99^(50) - 99.98^(50) + (99...

The value of ` 99^(50) - 99.98^(50) + (99*98)/(1*2) (97)^(50) -…+ 99 ` is

A

`0`

B

`-1`

C

`-2`

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `99^(50)-99.98^(50)+(99.98)/(1.2)(97)^(50)-....+99`
`=^(99)C_(0)99^(50)-^(99)C_(1)(99-1)^(50)+^(99)C_(2)(99-2)^(50)-....+^(99)C_(98)(99-98)^(50)+^(99)C_(99)(99-99)^(50)`
`=99^(50)('^(99)C_(0)-^(99)C_(1)+^(99)C_(2)-^(99)C_(3)+...)+^(50)C_(1)*99^(49)('^(99)C_(1)-2*^(99)C_(2)+3*^(99)C_(3)-....)+....`
`=0+0+0+....+0=0`
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