Evaluate $C^{100}_{20} + 2*C^{99}_{20} + 3*C^{98}_{20}+...+81C^{20}_{20}$
Can someone give me hints. Is there an binomial theorem involved? I cant see it
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Do you know how to evaluate $$C_{20}^{100}+C_{20}^{99}+C_{20}^{98}+\cdots+C_{20}^{20}?$$ – bof Sep 25 '16 at 05:57
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Yes leaving it in C form is fine. Nope i dont haha. Is there an identity? Possible just write for me an identity? – RStyle Sep 25 '16 at 05:57
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wow ok i found the identity. $C^r_r + C^{r+1}r + .. +C^n_r = C^{n+1}{r+1}$ – RStyle Sep 25 '16 at 06:21
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Possible duplicate: http://math.stackexchange.com/questions/1939505/prove-that-sum-k-0nkmk-choose-m-nmn1-choose-m1-mn1-choose-m2/1939932#1939932 – Sep 25 '16 at 12:21
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Sorry if its duplicate. Found the answer. Thanks @bof – RStyle Sep 25 '16 at 15:02