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The value of the expression { _{ }^{ k-1 }{ C } }_{ k-1 }+{ _

Question

The value of the expression $_{k - 1} C_{k - 1} +_{k} C_{k - 1} + ...._{n + k - 2} C_{k - 1}$ is given by :

_{n + k - 1} C_{k - 1}

_{n + k - 1} C_{k}

_{n + k} C_{k}

None of these

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Amelia Discussed

The value of the expression

_{k - 1} C_{k - 1} +_{k} C_{k - 1} + ...._{n + k - 2} C_{k - 1}

is given by :

13 mins ago

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13 mins ago

Text solutionVerified

We know,

m = k \sum n^{m} C_{r} =^{n + 1} C_{r + 1}

According to the question,

m = n + k - 2

r = k - 1

Sum of series is given by

=^{m + 1} C_{k + 1}

=^{n + k - 1} C_{k}

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Question Text	The value of the expression $_{k - 1} C_{k - 1} +_{k} C_{k - 1} + ...._{n + k - 2} C_{k - 1}$ is given by :
Answer Type	Text solution:1
Upvotes	150