The coefficient of \(x^{101}\) in the expression \((5+x)^{500}+x(5+x)^{499}+x^2(5+x)^{498}+\ldot....

Channel:
PW Solutions
Subscribers:
456,000
Published on ● Video Link: https://www.youtube.com/watch?v=gTBmc2vNTPA


Duration: 2:01
0 views
0

The coefficient of \(x^{101}\) in the expression \((5+x)^{500}+x(5+x)^{499}+x^2(5+x)^{498}+\ldots+x^{500}, x>0\), is πŸ“²PW App Link - https://bit.ly/YTAI_PWAP 🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2024-06-28If \(\sum_{r=0}^{25}\left\{{ }^{50} C_r \cdot{ }^{50-r} C_{25-r}\right\}=K\left({ }^{50} C_{25}\....
2024-06-28If \(\sum_{i=1}^{20}\left(\frac{{ }^{20} C_{i-1}}{{ }^{20} C_i+{ }^{20} C_{i-1}}\right)^3=\frac{....
2024-06-28If the sum of the coefficients of all even powers of \(x\) in the product \(\left(1+x+x^2+\ldots....
2024-06-28The coefficient of \(x^7\) in the expression \((1+x)^{10}+x(1+x)^9\) \(+x^2(1+x)^8+\ldots \ldots....
2024-06-28Let \(n\) be a positive integer. Let\[A=\sum_{k=0}^n(-1)^{k n} C_k\left[\left(\frac{1}{2}\right)....
2024-06-28For integers \(n\) and \(r\), let \(\left(\begin{array}{l}n \\ r\end{array}\right)= \begin{cases....
2024-06-28If the sum of the co-efficients of all the positive even powers of \(x\) in the binomial expansi....
2024-06-28The maximum value of the term independent of ' \(t\) ' in the expansion of \(\left(t x^{\frac{1}....
2024-06-28If the coefficient of \(a^7 b^8\) in the expansion of \((a+2 b+4 a b)^{10}\) is \(K .2^{16}\), t....
2024-06-28\[\text { If } \sum_{k=1}^{31}\left({ }^{31} C_k\right)\left({ }^{31} C_{k-1}\right)-\sum_{k=1}^....
2024-06-28The coefficient of \(x^{101}\) in the expression \((5+x)^{500}+x(5+x)^{499}+x^2(5+x)^{498}+\ldot....
2024-06-28A ratio of the \(5^{\text {th }}\) term from the beginning to the \(5^{\text {th }}\) term from ....
2024-06-28Let \((x+10)^{50}+(x-10)^{50}=a_0+a_1 x+a_2 x^2+\ldots+a_{50} x^{50}\), for \(x \in R\) : then \....
2024-06-28The total number of irrational terms in the binomial expansion of \(\left(7^{1 / 5}-3^{1 / 10}\r....
2024-06-28If the number of integral terms in the expansion of \(\left(3^{1 / 2}+5^{1 / 8}\right)^n\) is ex....
2024-06-28Let \(n \in N\) and \([x]\) denote the greatest integer less than or equal to \(x\). If the sum ....
2024-06-28The term independent of \(x\) in the expansion of \(\left[\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\fra....
2024-06-28The remainder when \(7^{2022}+3^{2022}\) is divided by 5 is:....
2024-06-28Let \(\left(1+x+2 x^2\right)^{20}=a_0+a_1 x+a_2 x^2+\ldots+a_{40} x^{40}\) then \(a_1+a_3+a_5+\l....
2024-06-28The total number of two digit numbers ' \(n\) ', such that \(3^n+7^n\) is a multiple of 10 , is....
2024-06-28If the coefficients of \(x\) and \(x^2\) in the expansion of \((1+x)^p\) \((1-x)^q, p, q \geq 15....