Find the sum of following series: (i) \( \sum_{r=1}^{51} r\left({ }^{(1001-r)} C_{950}\right) \)...

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Find the sum of following series:
(i) \( \sum_{r=1}^{51} r\left({ }^{(1001-r)} C_{950}\right) \)
(ii) \( \sum_{r=0}^{10} 100+r C_{r} \)
(iii) \( \sum_{r=0}^{20}{ }^{m+n+r} C_{r} \)
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