Expert answers to "Substitute n=1, 2, 3, 4, 5 and find..."

Jaya Legge

Answered question

2021-06-10

Substitute n=1, 2, 3, 4, 5 and find the first five sequences in sequence

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{n}}}

krolaniaN

Skilled2021-06-11Added 86 answers

Given

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{n}}}

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{1}}} = \frac{1}{2^{1}} = \frac{1}{2}

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{2}}} = \frac{1}{2^{1}} + \frac{1}{2^{2}} = \frac{1}{2} + \frac{1}{4}

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{3}}} = \frac{1}{2^{1}} + \frac{1}{2^{2}} + \frac{1}{2^{3}} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8}

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{4}}} = \frac{1}{2^{1}} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16}

{\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^{5}}} = \frac{1}{2^{1}} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}} = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}

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