Convert the following products into factorials: (iii) (n + 1) (n +2) (n + 3).... (2n) (iv) 1.3.5 . 7 . 9.... (2n-1)
Convert the following products into factorial: (n+1)(n+2)(n+3)(2n)
Assuming that 50 heavy (i.e., containing N^(15) ) DNA molecules replicated twice in a medium containing N^(14) we expect
Find the value of i^(n)+i^(n+1)+i^(n+2)+i^(n+3) for all n in N.
If I_(n)=int_(1)^(e)(ln x)^(n)dx(n is a natural number) then I_(2020)+nI_(m)=e, where n,m in N .The value of m+n is equal to
Sum of four consecutive powers of i(iota) is zero. i.e., i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0,forall n in I. If sum_(n=1)^(25)i^(n!)=a+ib, " where " i=sqrt(-1) , then a-b, is
Show that the linear function in n i.e. f(n)=an+b determines an arithmetic progression, where a,b are constants.
Let f: NvecN be defined by f(n)={(n+1)/2, "if" n "i s o d d"n/2, "if "n "i s e v e n" for a l l n N} Find whether the function f is bijective.
Prove that square of any even natural number i.e. (2n)^2 is equal to sum of n terms of a certain series of integers in A.P.
