Selesaikan {l}{a+b+c+d+m=1}{2^{4}a+2^{3}b+2^{2}c+2d+m=1/2}{3^{4}a+3^{3}b+3^{2}c+3d+m=1/3}{4^{4}a+4^{3}b+4^2c+4d+m=1/4}{5^4a+5^3b+5^2c+5d+m=1/5}

$$\left\{ \begin{array} { l } { a + b + c + d + m = 1 } \\ { 2 ^ { 4 } a + 2 ^ { 3 } b + 2 ^ { 2 } c + 2 d + m = \frac { 1 } { 2 } } \\ { 3 ^ { 4 } a + 3 ^ { 3 } b + 3 ^ { 2 } c + 3 d + m = \frac { 1 } { 3 } } \\ { 4 ^ { 4 } a + 4 ^ { 3 } b + 4 ^ { 2 } c + 4 d + m = \frac { 1 } { 4 } } \\ { 5 ^ { 4 } a + 5 ^ { 3 } b + 5 ^ { 2 } c + 5 d + m = \frac { 1 } { 5 } } \end{array} \right.$$

Selesaikan untuk a, b, c, d, m

$$a=\frac{1}{120}\approx 0.008333333$$

$$b=-\frac{1}{8}=-0.125$$

$$c=\frac{17}{24}\approx 0.708333333$$

$$d = -\frac{15}{8} = -1\frac{7}{8} = -1.875$$

$$m = \frac{137}{60} = 2\frac{17}{60} \approx 2.283333333$$