The numbers 1,3,6,10,15,21,28."……" are c...

The numbers `1,3,6,10,15,21,28."……"` are called triangular numbers. Let `t_(n)` denotes the bth triangular number such that `t_(n)=t_(n-1)+n,AA n ge 2`.
The value of `t_(50)` is

1075

1175

1275

1375

Text Solution

Verified by Experts

The correct Answer is:

Given sequece `1,3,6,10,15,21,28,"…"`
where `t_(n)=t_(n-1)+n,AA n ge 2`
So, `t_(n)=[t_(n-2)+(n-1)]+n`
`vdots " "vdots " " vdots " "`
`t_(n)=t_(1)+2+3+"........"+(n-1)+n`
`t_(n)=1+2+3+"......"+n`
`t_(n)=(n(n+1))/(2)`
`t_(50)=(50xx51)/(2)=25xx51=1275`.

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The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the n^(th) triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . The number of positive integers lying between t_(100) and t_(101) are

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The numbers 1,3,6,10,15,21,28."……" are called triangular numbers. Let t_(n) denotes the bth triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . If (m+1) is the nth triangular number, then (n-m) is

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