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11Alexandr11 [23.1K]
3 years ago
13

5 - 7 second power + 6 - 7 second power + 5 - 7 second power + 6 - 7 second power + 10 - 7 second power + 10 - 7 second power​

Mathematics
1 answer:
Zanzabum3 years ago
8 0

ANSWER: -252

HOW TO GET IT:

Simply follow PEMDAS. Solve each exponent first, then do the rest.

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Which of the following is equivalent to the expression below (x+3)(x+4)
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Answer:

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Step-by-step explanation:

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Start with the geometric power series LaTeX: 1+x+x^2+x^3+x^4+\cdots Substitute LaTeX: -x^3in place of LaTeX: x, and then take a
valina [46]

Answer:

-3x^2+6x^5-9x^8+12x^{11}+...=\sum_{n=1}^{\infty }\left ( -1 \right )^n\,\,3n\,\,x^{3n-1}

Step-by-step explanation:

Given : 1+x+x^2+x^3+x^4+\cdots

On putting -x^3 in place of x , we get 1+\left ( -x^3 \right )+\left ( -x^3 \right )^2+\left ( -x^3 \right )^3+\left ( -x^3 \right )^4+...

On simplifying , we get 1-x^3+x^6-x^9+x^{12}+...

On differentiating , we get \left ( 1-x^3+x^6-x^9+x^{12}+... \right )'=-3x^2+6x^5-9x^8+12x^{11}+...

Here ,

-3x^2=\left ( -1 \right )^1\,3(1)x^{3(1)-1}\\6x^5=\left ( -1 \right )^2\,\,3(2)\,\,x^{3(2)-1}\\-9x^8=\left ( -1 \right )^3\,\,3(3)\,\,x^{3(3)-1}\\12x^{11}=\left ( -1 \right )^4\,\,3(4)\,\,x^{3(4)-1}

Now , we need to express it using summation notation.

\left ( 1-x^3+x^6-x^9+x^{12}+... \right )'=-3x^2+6x^5-9x^8+12x^{11}+...=\sum_{n=1}^{\infty }\left ( -1 \right )^n\,\,3n\,\,x^{3n-1}

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