The sum of the series \( 1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots . \). to \...
The sum of the series \( 1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots . \). to \( n \) terms is
(a) \( n(n+1)(n+2) \)
(b) \( (n+1)(n+2)(n+3) \)
(c) \( \frac{1}{4} n(n+1)(n+2)(n+3) \)
(d) \( \frac{1}{4}(n+1)(n+2)(n+3) \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-07-03 | Greatest integer by which \( 1+\sum_{r=1}^{30} r \times r \) ! is divisible is
(a) Composite num... |
| 2023-07-03 | If the ratio of A.M. between two positive real numbers \( a \) and \( b \) to their H.M. is \( m... |
| 2023-07-03 | If \( A_{1}, A_{2} ; G_{1}, G_{2} \) and \( H_{1}, H_{2} \) be two A.M.s, G.M.s and H.M.s betwee... |
| 2023-07-03 | - (a) 1 (b) -1 - (c) 0 (d) None of these |
| 2023-07-03 | If the sum of first \( p \) terms, first \( q \) terms and first \( r \) terms of an A.P. be \( ... |
| 2023-07-03 | If \( a, b, c \) are in A.P. and \( |a|,|b|,|c|1 \), and
\[
\begin{array}{l}
x=1+a+a^{2}+\ldots ... |
| 2023-07-03 | if the sum of first p,q,r terms of an AP are \( a, b, c \) respectively then \( \frac{a}{p}(q-r)... |
| 2023-07-03 | If \( x, y, z \) are positive then the minimum value of \( x^{\log y-\log z}+y^{\log z-\log x}+z... |
| 2023-07-03 | If \( H \) be the \( H . M \). between \( a \& b \), then
(a) \( (H-2 a)(H-2 b)=H^{2} \)
(b) \( ... |
| 2023-07-03 | If \( a, b, c \) are in A.P. and \( x, y, z \) are in G.P., then find the value of \( x^{b-c} \c... |
| 2023-07-03 | The sum of the series \( 1 \cdot 2 \cdot 3+2 \cdot 3 \cdot 4+3 \cdot 4 \cdot 5+\ldots . \). to \... |
| 2023-07-03 | If \( \frac{a}{b}, \frac{b}{c}, \frac{c}{a} \) are in H.P., then
(a) \( a^{2} b, c^{2} a, b^{2} ... |
| 2023-07-03 | The sum of the series \( \frac{1}{3 \times 7}+\frac{1}{7 \times 11}+\frac{1}{11 \times 15}+\ldot... |
| 2023-07-03 | For any odd integer \( n \geq 1, n^{3}-(n-1)^{3}+\ldots+(-1)^{n-1} 1^{3}= \) |
| 2023-07-03 | If \( a, b, c \) are in G.P., then \( \log _{a} x, \log _{b} x, \log _{c} x \) are in
(a) A.P.
(... |
| 2023-07-03 | The sum to \( n \) terms of the series \( 1+3+7+15+31+\ldots \). is
(a) \( 2^{n+1}-n \)
(b) \( 2... |
| 2023-07-03 | If the A.M., G.M. and H.M. between two positive numbers \( a \) and \( b \) are equal, then
(a) ... |
| 2023-07-03 | If \( a, b, c \) are in A.P. \( b-a, c-b \) and a are in G.P., then \( a: b: c \) is
(a) \( 1: 2... |
| 2023-07-03 | The expression \( \left[x+\left(x^{3}-1\right)^{1 / 2}\right]^{5}+\left[x-\left(x^{3}-1\right)^{... |
| 2023-07-03 | Let the coefficients of the middle terms in the expansion of \( \left(\frac{1}{\sqrt{6}}+\beta x... |
| 2023-07-03 | The two geometric mean between the number 1 and 64 are
(a) 1 and 64
(b) 4 and 16
(c) 2 and 16
(d... |
0