SOLUTION: {{{a=1+2x+4x^2+..............}}}, where -1<2x<1, {{{b= 1+3y+9y^2+.............}}}, where -1<3y<1 and 3y+2x=1, prove that ab=a+b
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-> SOLUTION: {{{a=1+2x+4x^2+..............}}}, where -1<2x<1, {{{b= 1+3y+9y^2+.............}}}, where -1<3y<1 and 3y+2x=1, prove that ab=a+b
Log On
a = =
That's an infinite geometric series with first term t1 = 1,
and r = 2x. And since -1 < 2x < 1 it converges and we can use the formula:
= =
b = =
That's also an infinite geometric series with first term t1 = 3y,
and r = 3y. And since -1 < 3y < 1 we can use the formula:
= =
So
a = , b =
ab = · =
a + b = +{1/(1-3y)}}} = =
= =
and we are given that 3y+2x=1, so we replace(3y+2x) by 1
=
So ab and a + b both equal to
Edwin