If r=1∑nnCr3r is equal to 4095 then n equals.

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If _{r = 1}^{n} {^{n}C_{r}} 3^{r} is equal to 4095 then n equ

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If $r = 1 \sum n^{n} C_{r} 3^{r}$ is equal to $4095$ then $n$ equals.

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Sebastian Discussed

r = 1 \sum n^{n} C_{r} 3^{r}

is equal to

4095

then

n

equals.

13 mins ago

Discuss this question LIVE

13 mins ago

We have,

_{r = 1}^{n} \sum^{n} C_{r} = 4095

⟹^{n} C_{1} +^{n} C_{2} 3^{2} + ... .^{n} C_{n} 3^{n} = 4095

⟹ (1 + 3)^{n} -^{n} C_{0} = 4095

⟹ 4^{n} - 1 = 4095

⟹ 4^{n} = 4^{6}

⟹ n = 6

Hence, this is the answer.

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Question Text	If $r = 1 \sum n^{n} C_{r} 3^{r}$ is equal to $4095$ then $n$ equals.
Answer Type	Text solution:1
Upvotes	150