Pertanyaan

Nilai dari k = 1 ∑ 15 k + k k + k k + 1 1 = ....

Nilai dari $k = 1 \sum 15 \frac{1}{k + k k + k k + 1} = ....$

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat! Pada notasi sigma, bentuk dapat dijabarkan menjadi . Sehingga: Oleh karena itu, jawaban yang tepat adalah D.

Ingat!

Pada notasi sigma, bentuk sum from i equals 1 to n of U subscript i dapat dijabarkan menjadi .

Sehingga:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sum from k equals 1 to 15 of fraction numerator 1 over denominator square root of k plus k square root of k plus k square root of k plus 1 end root end fraction end cell row blank equals cell sum from k equals 1 to 15 of fraction numerator 1 over denominator square root of k open parentheses 1 plus k close parentheses plus k square root of k plus 1 end root end fraction end cell row blank equals cell sum from k equals 1 to 15 of fraction numerator 1 over denominator square root of k square root of k plus 1 end root open parentheses square root of k plus 1 end root plus square root of k close parentheses end fraction end cell row blank equals cell sum from k equals 1 to 15 of fraction numerator 1 over denominator square root of k square root of k plus 1 end root open parentheses square root of k plus 1 end root plus square root of k close parentheses end fraction cross times fraction numerator square root of k plus 1 end root minus square root of k over denominator square root of k plus 1 end root minus square root of k end fraction end cell row blank equals cell sum from k equals 1 to 15 of fraction numerator square root of k plus 1 end root minus square root of k over denominator square root of k times square root of k plus 1 end root end fraction end cell row blank equals cell sum from k equals 1 to 15 of fraction numerator up diagonal strike square root of k plus 1 end root end strike over denominator square root of k times up diagonal strike square root of k plus 1 end root end strike end fraction minus fraction numerator up diagonal strike square root of k end strike over denominator up diagonal strike square root of k end strike times square root of k plus 1 end root end fraction end cell row blank equals cell sum from k equals 1 to 15 of fraction numerator 1 over denominator square root of k end fraction minus fraction numerator 1 over denominator square root of k plus 1 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 1 end fraction minus fraction numerator 1 over denominator square root of 1 plus 1 end root end fraction plus fraction numerator 1 over denominator square root of 2 end fraction minus fraction numerator 1 over denominator square root of 2 plus 1 end root end fraction plus fraction numerator 1 over denominator square root of 3 end fraction minus fraction numerator 1 over denominator square root of 3 plus 1 end root end fraction plus end cell row blank blank cell... space plus fraction numerator 1 over denominator square root of 15 end fraction minus fraction numerator 1 over denominator square root of 15 plus 1 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 1 end fraction minus up diagonal strike fraction numerator 1 over denominator square root of 2 end fraction end strike plus up diagonal strike fraction numerator 1 over denominator square root of 2 end fraction end strike minus up diagonal strike fraction numerator 1 over denominator square root of 3 end fraction end strike plus up diagonal strike fraction numerator 1 over denominator square root of 3 end fraction end strike minus... plus up diagonal strike fraction numerator 1 over denominator square root of 15 end fraction end strike minus fraction numerator 1 over denominator square root of 16 end fraction end cell row blank equals cell 1 minus 1 fourth end cell row blank equals cell 3 over 4 end cell row blank equals cell 0 comma 75 end cell end table end style$

Oleh karena itu, jawaban yang tepat adalah D.

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