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2 years ago

Given m n, find the value of x and y m (7x+18) (5x-6) (3y+11) n

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

6 0

Answer:

$7x + 18 + 5x - 6 = 180 \\ 12x + 12 = 180 \\ 12x = 180 - 12 = 168 \\ x = 168 \div 12 =14 \\ 3y + 11 = 7x + 18 = 7 \times 14 + 18 \\ 3y + 11 = 98 + 18 = 116 \\ 3y = 116 - 11 = 105 \\ y = 105 \div 3 = 35$

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2 years ago

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The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

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Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

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