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The value of underset(i=1)overset(n)Sigm...

The value of `underset(i=1)overset(n)Sigmaunderset(j=1)overset(i)Sigmaunderset(k=1)overset(j)` =220, then the value of n equals

A

`11`

B

`12`

C

`10`

D

`9`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `sum_(i=1)^(n)sum_(j=1)^(i)sum_(k=1)^(j)1`
`=sum_(i=1)^(n)sum_(j=1)^(i)j`
`=sum_(i=1)^(n)(i(i+1))/(2)`
`=(1)/(2)sum_(i=1)^(n)(i^(2)+i)`
`=(n(n+1)(n+2))/(6)=220`
`:.n=10`
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