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f(n)=sum(x=1)^(n)[r^(2)(^(n)C(r)-^(n)C(r...

f(n)=sum_(x=1)^(n)[r^(2)(^(n)C_(r)-^(n)C_(r-1))+(2r+1)(^(n)C_(z))]," then "

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f(n)=sum_(r=1)^(n)[r^(2)(*^(n)C_(r)-^(n)C_(r-1))+(2r+1)^(n)C_(r)] then f(30) is

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If f(x)=sum_(r=1)^(n) { r^(2) (""^(n)C_(r)- ^(n) C_(r-1))+ (2r+1) ^(n) C_(r)} and f(30)=30(2)^(lambda), then the value of lambda is

If f(x)=sum_(r=1)^(n) { r^(2) (""^(n)C_(r)- ^(n) C_(r-1))+ (2r+1) ^(n) C_(r)} and f(30)=30(2)^(lambda), then the value of lambda is

If n is a positive integer, prove that sum_(r=1)^(n)r^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

Let f(n)=sum_(r=1)^(n)r^(2)C_(r)^(2)* Then ,f(5)=