If `nger`, then
`""^(r)C_(r)+""^(r+1)C_(r)+""^(r+2)C_(r)+......+""^(n)C_(r)` is equal to

Options

A. `""^(n+1)C_(r)`
B. `""^(n+1)C_(r+1)`
C. `""^(n+2)C_(r+1)`
D. `""^(n+2)C_(r+2)`

Explanation

To solve the problem, we need to evaluate the sum:

\[ \sum_{k=r}^{n} \binom{k}{r} \]

This can be expressed as:

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