substitution-method

Consider the following recurrence relation : $$T(n)=2 T(n-1)+n 2^n \text { for } n>0, T(0)=1$$ Which ONE of the following options is CORRECT?

Consider the following recurrence relation: $$T(n) = \begin{cases} \sqrt{n} T(\sqrt{n}) + n & \text{for } n \ge 1, \\ 1 & \text{for } n = 1. \end{cases}$$ Which one of the followin...

For parameters a and b, both of which are $$\omega \left( 1 \right)$$, T(n) = $$T\left( {{n^{1/a}}} \right) + 1$$, and T(b) = 1. Then T(n) is

The value of $$\int_0^{\pi /4} {x\cos \left( {{x^2}} \right)dx} $$ correct to three decimal places (assuming that $$\pi = 3.14$$ ) is ________.

$$\,\int\limits_{1/\pi }^{2/\pi } {{{\cos \left( {1/x} \right)} \over {{x^2}}}dx = } $$ __________.

Consider the following recurrence: $$T\left( n \right){\rm{ }} = {\rm{ 2T(}}\left\lceil {\sqrt n } \right\rceil {\rm{) + }}\,{\rm{1 T(1) = 1}}$$ Which one of the following is true?

The recurrence equation T(1) = 1 T(n) = 2T(n - 1)+n, $$n \ge 2$$ Evaluates to

The recurrence equation $$\,\,\,\,\,\,\,T\left( 1 \right) = 1$$ $$\,\,\,\,\,\,T\left( n \right) = 2T\left( {n - 1} \right) + n,\,n \ge 2$$ evaluates to

The solution to the recurrence equation T(2 k ) = 3 T(2 k-1 ) + 1, T (1) = 1, is:

Solve the following recurrence relation $$\,\,\,\,\,\,\,{x_n} = 2{x_{n - 1}} - 1\,\,n > 1$$ $$\,\,\,\,\,\,\,{x_1} = 2$$

Find a solution to the following recurrence equation T(n) = T(n - 1)+ n T(1) = 1

Solve the recurrence equations T (n) = T (n - 1) + n T (1) = 1