{ }^{34} C_5+sum_{r=0}^4{ }^{(38-r)} C_4= | vedclass

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(B) Given expression: ${ }^{34} C_5+\sum_{r=0}^4{ }^{(38-r)} C_4$ Expanding the summation: ${ }^{34} C_5+{ }^{38} C_4+{ }^{37} C_4+{ }^{36} C_4+{ }^{3

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${ }^{39} C_5$

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(B) Given expression: ${ }^{34} C_5+\sum_{r=0}^4{ }^{(38-r)} C_4$ Expanding the summation: ${ }^{34} C_5+{ }^{38} C_4+{ }^{37} C_4+{ }^{36} C_4+{ }^{35} C_4+{ }^{34} C_4$ Using the identity ${ }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r$: ${ }^{34} C_5+{ }^{34} C_4 = { }^{35} C_5$ Now,${ }^{35} C_5+{ }^{35} C_4 = { }^{36} C_5$ Then,${ }^{36} C_5+{ }^{36} C_4 = { }^{37} C_5$ Then,${ }^{37} C_5+{ }^{37} C_4 = { }^{38} C_5$ Finally,${ }^{38} C_5+{ }^{38} C_4 = { }^{39} C_5$ Thus,the result is ${ }^{39} C_5$.

${ }^{34} C_5+\sum_{r=0}^4{ }^{(38-r)} C_4=$

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