Math, asked by Anonymous, 15 days ago

PLEASE ANSWER MY QUESTION​

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Answers

Answered by sajan6491
12

\sum_{n=4}^{8} \left(x^{2} - \frac{9 \cosh^{2}{\left(f n \right)}}{\sinh^{2}{\left(f n \right)}}\right)

Simplify:

{\sum_{n=4}^{8} \left(x^{2} - \frac{9 \cosh^{2}{\left(f n \right)}}{\sinh^{2}{\left(f n \right)}}\right)=\sum_{n=4}^{8} \left(x^{2} - \frac{9}{\tanh^{2}{\left(f n \right)}}\right)}

Since the bounds are finite, the number of terms is finite as well, and we just calculate the sum by summing up the terms.

{\color{red}{\sum_{n=4}^{8} \left(x^{2} - \frac{9}{\tanh^{2}{\left(f n \right)}}\right)}=\color{red}{\left(\left(x^{2} - \frac{9}{\tanh^{2}{\left(4 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(5 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(6 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(7 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(8 f \right)}}\right)\right)}}

{\color{red}{\sum_{n=4}^{8} \left(x^{2} - \frac{9}{\tanh^{2}{\left(f n \right)}}\right)}=\color{red}{\left(5 x^{2} - \frac{9}{\tanh^{2}{\left(8 f \right)}} - \frac{9}{\tanh^{2}{\left(7 f \right)}} - \frac{9}{\tanh^{2}{\left(6 f \right)}} - \frac{9}{\tanh^{2}{\left(5 f \right)}} - \frac{9}{\tanh^{2}{\left(4 f \right)}}\right)}}

Hence,

{\sum_{n=4}^{8} \left(x^{2} - \frac{9 \cosh^{2}{\left(f n \right)}}{\sinh^{2}{\left(f n \right)}}\right)=5 x^{2} - \frac{9}{\tanh^{2}{\left(8 f \right)}} - \frac{9}{\tanh^{2}{\left(7 f \right)}} - \frac{9}{\tanh^{2}{\left(6 f \right)}} - \frac{9}{\tanh^{2}{\left(5 f \right)}} - \frac{9}{\tanh^{2}{\left(4 f \right)}}}

Answered by OoAryanKingoO78
2

Answer:

\sum_{n=4}^{8} \left(x^{2} - \frac{9 \cosh^{2}{\left(f n \right)}}{\sinh^{2}{\left(f n \right)}}\right)

Simplify:

{\sum_{n=4}^{8} \left(x^{2} - \frac{9 \cosh^{2}{\left(f n \right)}}{\sinh^{2}{\left(f n \right)}}\right)=\sum_{n=4}^{8} \left(x^{2} - \frac{9}{\tanh^{2}{\left(f n \right)}}\right)}

Since the bounds are finite, the number of terms is finite as well, and we just calculate the sum by summing up the terms.

{\color{red}{\sum_{n=4}^{8} \left(x^{2} - \frac{9}{\tanh^{2}{\left(f n \right)}}\right)}=\color{red}{\left(\left(x^{2} - \frac{9}{\tanh^{2}{\left(4 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(5 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(6 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(7 f \right)}}\right) + \left(x^{2} - \frac{9}{\tanh^{2}{\left(8 f \right)}}\right)\right)}}

{\color{purple}{\sum_{n=4}^{8} \left(x^{2} - \frac{9}{\tanh^{2}{\left(f n \right)}}\right)}=\color{red}{\left(5 x^{2} - \frac{9}{\tanh^{2}{\left(8 f \right)}} - \frac{9}{\tanh^{2}{\left(7 f \right)}} - \frac{9}{\tanh^{2}{\left(6 f \right)}} - \frac{9}{\tanh^{2}{\left(5 f \right)}} - \frac{9}{\tanh^{2}{\left(4 f \right)}}\right)}}

Hence,

{\sum_{n=4}^{8} \left(x^{2} - \frac{9 \cosh^{2}{\left(f n \right)}}{\sinh^{2}{\left(f n \right)}}\right)=5 x^{2} - \frac{9}{\tanh^{2}{\left(8 f \right)}} - \frac{9}{\tanh^{2}{\left(7 f \right)}} - \frac{9}{\tanh^{2}{\left(6 f \right)}} - \frac{9}{\tanh^{2}{\left(5 f \right)}} - \frac{9}{\tanh^{2}{\left(4 f \right)}}}

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