If {a_{n}} and {b_{n}} are geometric sequences with common ratios of r₁ and r₂, is {a_{n}b_{n}} a geometric sequence too? If yes, what is the common ratio?

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05-05-2014
Mathematics

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If {a_{n}} and {b_{n}} are geometric sequences with common ratios of r₁ and r₂, is {a_{n}b_{n}} a geometric sequence too? If yes, what is the common ratio?

Sagot :

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Crisforpidn Crisforpidn · Answer 1 · 2014-05-06T02:54:16-04:00

Crisforpidn Crisforpidn

06-05-2014

a_{n+1}b_{n+1} / a_{n}b_{n} =( a_{n+1} / a_{n}) * ( b_{n+1} / b_{n} ) = ( r1 ) * ( r2) =>
{a_{n}b_{n}} a geometric sequence; the common ratio is ( r1 ) * ( r2) .

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