If \( \lim _{n \rightarrow \infty} \frac{\left[1^{3}+2^{3}+3^{3} \ldots . .+(2 n)^{3}\right] \cd...
If \( \lim _{n \rightarrow \infty} \frac{\left[1^{3}+2^{3}+3^{3} \ldots . .+(2 n)^{3}\right] \cdot\left[1^{4}+2^{4}+\ldots .(3 n)^{4}\right]}{\left[1^{8}+2^{8}+3^{8} \ldots \ldots+(4 n)^{8}\right]}=\frac{3^{a}}{2^{b} \cdot 5} \) then \( a+b \) is
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | Let \( \operatorname{In}(x)=\int_{0}^{x} \frac{1}{\left(t^{2}+5\right)^{n}} d t, n=1,2,3, \ldots... |
| 2023-06-09 | Let \( f:(0,2) \rightarrow R \) be defined as \( f(x)=\log _{2}\left(1+\tan \left(\frac{\pi x}{4... |
| 2023-06-09 | Find the number of values of \( x \) satisfying \( \int_{0}^{\pi} t^{2} \sin (x-t) d t \) \( =x^... |
| 2023-06-09 | Let \( f(x)=2+|x|-|x-2|+|x+1|, x \in R \). Consider
\( (\mathrm{S}-1): f^{\prime}\left(-\frac{3}... |
| 2023-06-09 | Let \( F:[3,5] \rightarrow R \) be a twice differentiable function on (3,
5) such that \( F(x)=e... |
| 2023-06-09 | The minimum value of the twice differentiable function \( f(x) \) \( =\int_{0}^{x} e^{x-t} f^{\p... |
| 2023-06-09 | Given that \( U_{n}=\{x(1-x)\}^{n} \) and \( n \geq 2 \) and
\[
\frac{d^{2} U_{n}}{d x^{2}}=n(n-... |
| 2023-06-09 | \( \int_{1 / 3}^{1 / 2}\left\{x\left[\frac{2}{x}\right]\right\} d x \) (where [·] is G.I.F.) and... |
| 2023-06-09 | If \( f(x)=x+\int_{0}^{1}\left(x y^{2}+x^{2} y\right)(f(y)) d y \), find \( f(x) \) |
| 2023-06-09 | Let \( f(x)=x^{3}-\frac{3 x^{2}}{2}+x+\frac{1}{4} \). Find the value of \( \left(\int_{1 / 5}^{4... |
| 2023-06-09 | If \( \lim _{n \rightarrow \infty} \frac{\left[1^{3}+2^{3}+3^{3} \ldots . .+(2 n)^{3}\right] \cd... |
| 2023-06-09 | Let \( f \) be a real-valued function defined on the interval \( (0, \infty) \) by \( f(x)=\ln x... |
| 2023-06-09 | \( I=\int_{\pi / 4}^{2 n \pi+\frac{\pi}{4}} \frac{d x}{\left(1+\pi^{\cos x}\right)\left(1+\pi^{\... |
| 2023-06-09 | Let \( f(x)=\left\{\begin{array}{ll}x+1, & 0 \leq x \leq 1 \\ 2 x^{2}-6 x+6, & 1x \leq 2\end{arr... |
| 2023-06-09 | If \( \lim _{n \rightarrow \infty}\left(\frac{{ }^{3 n} C_{n}}{{ }^{2 n} C_{n}}\right)^{1 / n}=\... |
| 2023-06-09 | If \( \int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2} \) then match the following Column-I... |
| 2023-06-09 | Consider a parabola \( y=\frac{x^{2}}{4} \) and the point \( F(0,1) \).
Let \( A_{1}\left(x_{1},... |
| 2023-06-09 | Suppose that the function \( f, g, f^{\prime} \) and \( g^{\prime} \) are continuous over \( [0,... |
| 2023-06-09 | If \( U_{n}=\int_{0}^{\frac{\pi}{2}} \cos ^{n} x \cos n x d x \) then
(a) \( U_{1}, U_{2} \ldots... |
| 2023-06-09 | If \( \int_{0}^{1}\left(\sum_{k=1}^{2014} \frac{x^{2}}{x^{3}+k^{3}}\right)\left(\prod_{k=1}^{201... |
| 2023-06-09 | If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), ... |
0