\( \lim _{n \rightarrow \infty} \frac{\left(1^{k}+2^{k}+3^{k}+\ldot...
\( \lim _{n \rightarrow \infty} \frac{\left(1^{k}+2^{k}+3^{k}+\ldots . .+n^{k}\right)}{\left(1^{2}+2^{2}+\ldots . .+n^{2}\right)\left(1^{3}+2^{3}+\ldots \ldots . .+n^{3}\right)}=F(k) \), then \( (k \in N) \)
(A) \( F(k) \) is finite for \( k \leq 6 \)
(B) \( F(5)=0 \)
(C) \( F(6)=\frac{12}{7} \)
(D) \( F(6)=\frac{5}{7} \)
\( \mathrm{P}_{\mathrm{P}} \)
W
📲 PW App Link - https://bit.ly/YTAI_PWAP
🌐 PW Website - https://www.pw.live/
Other Videos By PW Solutions
| 2023-02-25 | If length of perpendicular drawn from points of a curve to a straig... |
| 2023-02-25 | Let \( g(t)=\int_{x_{1}}^{x_{2}} f(t, x) d x \). Then \( g^{\prime}... |
| 2023-02-25 | Let \( f:(0,1) \rightarrow R \) be defined by \( f(x)=\frac{b-x}{1-... |
| 2023-02-25 | If length of perpendicular drawn from points of a curve to a straig... |
| 2023-02-25 | Area bsunded by \( y=\sin ^{-1} x, y=\cos ^{-1} x, y=0 \) in first ... |
| 2023-02-25 | The graph of the function \( f(x)=\lim _{t \rightarrow 0}\left(\fra... |
| 2023-02-25 | Area bounded by \( y=x^{2}-2|x| \) and \( y=-1 \) is equal to
(A) \... |
| 2023-02-25 | If \( y=\int_{u(x)}^{v(x)} f(t) d t \), let us define \( \frac{d y}... |
| 2023-02-25 | If \( y=\int_{v(x)}^{v(x)} f(t) d t \), let us define \( \frac{d y}... |
| 2023-02-25 | Let \( f(a, b)=\int_{a}^{b}\left(x^{2}-4 x+3\right) d x,(ba) \) the... |
| 2023-02-25 | \( \lim _{n \rightarrow \infty} \frac{\left(1^{k}+2^{k}+3^{k}+\ldot... |
| 2023-02-25 | If \( F(x)=\int_{1}^{x} e^{t^{2} / 2}\left(1-t^{2}\right) d t \), t... |
| 2023-02-25 | Let \( f(x)=\int_{0}^{x}|2 t-3| d t \), then \( f \) is
(A) continu... |
| 2023-02-25 | Let \( A=\int_{1}^{e^{2}} \frac{\ell n x}{\sqrt{x}} d x \), then
(A... |
| 2023-02-25 | Given \( f \) is an odd function defined everywhere, periodic with ... |
| 2023-02-25 | Let \( f(x) \) be a continuous function and \( I=\int_{1}^{9} \sqrt... |
| 2023-02-25 | Column - I
Column - II
(A) Area bounded by region \( 0 \leq y \leq ... |
| 2023-02-25 | If \( t(x)=2^{[x \mid} \), where \( \{x\} \) denotes the fractional... |
| 2023-02-25 | Let \( f(x)=2 x^{3}-15 x^{2}+24 x \) and \( g(x)=\int_{0}^{x} f(t) ... |
| 2023-02-25 | Which of the following is true?
(A) Numbur of roots of the equation... |
| 2023-02-25 | The value of integral \( \int_{a}^{b} \frac{|x|}{x} d x, ab \) is:
... |
1