If `sum_(k=1)^n4(k-3)=A n^2+B n+C , n in N` then `|A+B-C|` equals

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

If sum_(k=1)^n(sum_(m=1)^k m^2)=a n^4+b n^3+c n^2+dn+e then -

Let f(n)=sum_(k=1)^(n) k^2(n C_k)^ 2 then the value of f(5) equals

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

Let a, b, c, d be real numbers such that sum_(k=1)^(n) (ak^(3) + bk^(2) + ck + d) = n^(4) or every natural number n. Then | a | + | b | + | C | + | d | is equal to

If for n in N ,sum_(k=0)^(2n)(-1)^k(^(2n)C_k)^2=A , then find the value of sum_(k=0)^(2n)(-1)^k(k-2n)(^(2n)C_k)^2dot

If for n in N ,sum_(k=0)^(2n)(-1)^k(^(2n)C_k)^2=A , then find the value of sum_(k=0)^(2n)(-1)^k(k-2n)(^(2n)C_k)^2dot

If sum_(n=1)^(5)(1)/(n(n+1)(n+2)(n+3))=(k)/(3), then k is equal to :-