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For any positive integer (m,n) (with nge...

For any positive integer (m,n) (with `ngeqm`), Let `((n),(m)) =.^nC_m` Prove that `((n),(m)) + 2((n-1),(m))+3((n-2),(m))+....+(n-m+1)((m),(m))`=`((n+2),(m+2))`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
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  14. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to a. x...

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  16. (n+2)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^(n-1))-.... is equal to

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  17. The value of sum(r=0)^(50)(-1)^r((50)Cr)/(r+2) is equal to a . 1/(50x...

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  18. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be a...

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