If each coefficient in the expansion of the expression $x (1 + x)^{n} (n ϵ N)$ in powers of 'x' is divided by the exponent of corresponding power, then the sum of the values thus obtained is equal to

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Solution

The correct option is D
$\frac{c_{0}}{1} + \frac{c_{1}}{2} + \frac{c_{2}}{3} + . . . . + \frac{c_{n - 1}}{n} + \frac{c_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}$

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If each coefficient in the expansion of the expression x(1+x)n(nϵN) in powers of 'x' is divided by the exponent of corresponding power, then the sum of the values thus obtained is equal to

The correct option is D c01+c12+c23+....+cn−1n+cnn+1=2n+1−1n+1

If each coefficient in the expansion of the expression $x (1 + x)^{n} (n ϵ N)$ in powers of 'x' is divided by the exponent of corresponding power, then the sum of the values thus obtained is equal to

The correct option is D
$\frac{c_{0}}{1} + \frac{c_{1}}{2} + \frac{c_{2}}{3} + . . . . + \frac{c_{n - 1}}{n} + \frac{c_{n}}{n + 1} = \frac{2^{n + 1} - 1}{n + 1}$