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Maths-

General

Easy

Question

The sum of series $1 plus fraction numerator 4 over denominator 5 end fraction plus fraction numerator 7 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 10 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$ is

7/16
5/16
105/64
35/16

The correct answer is: 35/16

Let,
$S equals 1 plus fraction numerator 4 over denominator 5 end fraction plus fraction numerator 7 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 10 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$
Then,
$fraction numerator 1 over denominator 5 end fraction S equals fraction numerator 1 over denominator 5 end fraction plus fraction numerator 4 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 7 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity$
$rightwards double arrow S open parentheses 1 minus fraction numerator 1 over denominator 5 end fraction close parentheses equals 1 plus 3 open square brackets fraction numerator 1 over denominator 5 end fraction plus fraction numerator 1 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 5 to the power of 3 end exponent end fraction plus horizontal ellipsis infinity close square brackets$
$rightwards double arrow fraction numerator 4 over denominator 5 end fraction S equals 1 plus 3 cross times fraction numerator 1 divided by 5 over denominator 1 minus left parenthesis 1 divided by 5 right parenthesis end fraction equals 1 plus fraction numerator 3 over denominator 4 end fraction equals fraction numerator 7 over denominator 4 end fraction$
$rightwards double arrow S equals fraction numerator 35 over denominator 16 end fraction$

Related Questions to study

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