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(.^(50)C(1))^(2)+2(.^(50)C(2))^(2)+3(.^(...

`(.^(50)C_(1))^(2)+2(.^(50)C_(2))^(2)+3(.^(50)C_(3))^(2)+.....+50(.^(50)C_(50))^(2)=`

A

`.^(100)C_(50)`

B

`50.(.^(100)C_(50))`

C

`25(.^(100)C_(50))`

D

`(2^(49))/(49!)(1.3.35…..99)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
`S = 0.(.^(50)C_(50))^(2) + 1.(.^(50)C_(1))^(2) + ….. + 50(.^(50)C_(50))^(2) …..(1)`
`S = 50(.^(50)C_(50))^(2) + 49(.^(50)C_(49))^(2) + ……. + U(.^(60)C_(0))^(2) …..(2)`
`(1) + (2)`
`S = 25[(.^(50)C_(0))^(2) + (.^(50)C_(1))^(2) + ….. + (.^(50)C_(50))]^(2))`
`= 25.(.^(100)C_(50))`
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