The coefficient of xk(0≤k≤n) in the expansion of 1+(1+x)+(1+x) 2+...........+(1+x) n is

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The coefficient of {x}^{k}( 0 k n ) in the expansion of 1+( 1+

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The coefficient of $x^{k} (0 \leq k \leq n)$ in the expansion of $1 + (1 + x) + (1 + x)^{2} + ........... + (1 + x)^{n}$ is

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Lucas Discussed

The coefficient of

x^{k} (0 \leq k \leq n)

in the expansion of

1 + (1 + x) + (1 + x)^{2} + ........... + (1 + x)^{n}

7 mins ago

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7 mins ago

1 + (1 + x) + (1 + x)^{2} + ..... + (1 + x)^{n}

∴

coefficient of

x^{k} =_{0} C_{k} +_{1} C_{k} +_{2} C_{k} + ...... +_{n} C_{k}

=_{0} C_{k + 1}_{0} C_{k} +_{1} C_{k} +_{2} C_{k} + ...... +_{n} C_{k}

=_{1} C_{k + 1} +_{1} C_{k} +_{2} C_{k} + ...... +_{n} C_{k}

=_{2} C_{k + 1} +_{2} C_{k} + ...... +_{n} C_{k}

=^{n + 1} C_{k + 1}

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Question Text	The coefficient of $x^{k} (0 \leq k \leq n)$ in the expansion of $1 + (1 + x) + (1 + x)^{2} + ........... + (1 + x)^{n}$ is
Answer Type	Text solution:1
Upvotes	150