1-find-u-the-value-of-u-if-n-1-4-2u-2-n-1-64-2-find-k-if-n-1-k-1-3-n-1-2-3-

Question Number 32707 by Rio Mike last updated on 31/Mar/18

1) find u the value of u if

\sum_{n = 1}^{4} 2 u . 2^{n - 1} = 64

2) find k if

\sum_{n = 1}^{\infty} k . {(\frac{1}{3})}^{n - 1} = \frac{2}{3}

Answered by MJS last updated on 31/Mar/18

\underset{n = 1}{\sum^{4}} 2 u \times 2^{n - 1} = 2 u \underset{n = 1}{\sum^{4}} 2^{n - 1} =

= 2 u (1 + 2 + 4 + 8) = 30 u

u = \frac{64}{30} = \frac{32}{15}

\underset{n = 1}{\sum^{\infty}} k \times {(\frac{1}{3})}^{n - 1} = k \underset{n = 0}{\sum^{\infty}} \frac{1}{3^{n}} = k \times \frac{3}{2}

\frac{3 k}{2} = \frac{2}{3}

k = \frac{4}{9}

Commented by NECx last updated on 02/Apr/18

h o w d i d \underset{n = 0}{\sum^{\propto}} k \times {(1 / 3)}^{n - 1} b e c o m e 3 k / 2

? ? ?

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