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Tcecarenko [31]

3 years ago

6

What is the value of the expression 2106÷162? What is the value of the expression 2106÷162? What is the value of the expression

2106÷162?

1 answer:

finlep [7]3 years ago

7 0

Answer:

13

Step-by-step explanation:

The value of the expression of 2106÷162 can be calculated as follows

= 2106÷162

= 13

Hence the value of the expression 2106 ÷ 162 is 13

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Combine like terms : 2x+5x+10x

8090 [49]

Answer: =17x

Step-by-step explanation: hope this help, hope you understand it too.

Let's simplify step-by-step.

2x+5x+10x

Combine Like Terms:

=2x+5x+10x

=(2x+5x+10x)

=17x

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3 years ago

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Setler79 [48]

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7 0

3 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

4 years ago