Question

Find the value of $C_0+\frac{C_{1}X}{2}+\frac{C_2{X}^2}{3}+...+\frac{C_n{X}^n}{n+1}$

Answer 1

$C_0+\frac{C_{1}x}{2}+\frac{C_2{x}^2}{3}+....+\frac{C_x{x}^n}{n+1}$
$(1+x{)}^n=C_0+C_{1}x+C_2{x}^{2}f.....+C_n{x}^n$
fakiy dx & integrate both s 1 dx
$\int (1+x{)}^{x}dx=\int (a+ax+C_2{x}^{2}y...+C_n{x}^x)dx$
$\frac{(1+x{)}^{n+1}}{n+1}=C_{0}x+\frac{C_1{x}^2}{2}+\frac{C_2{x}^3}{3}+....+\frac{C_x{x}^{n+1}}{n+1}$
$\frac{(1+x{)}^{n+1}}{(n+1)}=c(C_0+\frac{C_{1}x}{2}+\frac{C_2{x}^2}{3}+...+\frac{C_n{x}^n}{n+1})$
$C_0+\frac{C_{1}x}{2}+\frac{C_2{x}^2}{3}+...+\frac{C_x{x}^n}{n+1}=\frac{(1+x{)}^{n+1}}{x(n+1)}$