Find the sequence of the numbers defined by `a_n={1/n ,` when n is odd `-1/n` , when n is even

A function f from the set of natural numbers N to the set of integers Z is defined by f(n)={((n-1)/(2),"when n is odd"),(-(n)/(2),"when n is even"):} Then f(n) is -

Find the 5th and 10th terms of the sequence [u_(n)] defined by, u_(n) = {(2n+7 "when n is odd"),(n^(2) + 1 "when n is even"):}

Find the 25th and 50th terms of the sequence whose nth terms is given by u_(n) = {((n)/(n+1) "when n is odd"),((n+1)/(n+2) "when n is even"):}

Find the sum of n terms of the sequence (a_n),w h e r e a_n=5-6n ,n in Ndot

Consider the sequence defined by a_n=a n^2+b n+c dot If a_1=1,a_2=5,a n da_3=11 , then find the value of a_(10)dot

Let the sequence a_n be defined as follows: a_1 = 1, a_n = a_(n - 1) + 2 for n ge 2 . Find first five terms and write corresponding series

A mappin f : N rarrN where N is the set of natural numbers is defined as f(n)=n^(2) for n odd f(n)=2n+1 for n even for n inN . Then f is

let NN be the set of natural numbers and f: NN uu {0} rarr NN uu [0] be definedby : f(n)={(n+1 " when n is even" ),(n-1" when n is odd " ):} Show that ,f is a bijective mapping . Also that f^(-1)=f

If composite function f_1(f_2(f_3((f_n(x))))n timesis an decreasing function and if 'r' functions out of total 'n' functions are decreasing function while rest are increasing, then the maximum value of r(n-r) is (a) (n^2-4)/4 , when n is of the form 4k (b) (n^2)/4, when n is an even number (c) (n^2-1)/4, when n is an odd number (d) (n^2)/4, when n is of the form 4k+2

Let f: N to N be defined by f (n) = {{:((n +1)/( 2 ), if n " is odd" ), ( (n)/(2), "if n is even "):} for all n in N. State whether the function f is bijective. Justify your answer.