Pertanyaan

Jika 1 + 2 1 + 2 + 3 1 + 3 + 4 1 + ⋯ + 1.000.000 + 1.000.001 1 = a − b ,maka nilai a - b adalah ….

Jika $\frac{1}{1 + 2} + \frac{1}{2 + 3} + \frac{1}{3 + 4} + \dots + \frac{1}{1.000.000 + 1.000.001} = a - b$ , maka nilai a - b adalah ….

999.999
1.000.000
1.000.001

A. Triagrina

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Ingat kembali merasionalkan bentuk akar didapat Sehingga Karena diketahui , maka nilai a - b = 1.000.001- 1 = 1.000.000. Jadi, jawaban yang tepat adalah B.

Ingat kembali merasionalkan bentuk akar

didapat

$begin mathsize 11px style fraction numerator 1 over denominator square root of 1 plus square root of 2 end fraction cross times fraction numerator square root of 1 minus square root of 2 over denominator square root of 1 minus square root of 2 end fraction equals fraction numerator square root of 1 minus square root of 2 over denominator 1 minus 2 end fraction equals negative left parenthesis square root of 1 minus square root of 2 right parenthesis equals square root of 2 minus square root of 1 fraction numerator 1 over denominator square root of 2 plus square root of 3 end fraction cross times fraction numerator square root of 2 minus square root of 3 over denominator square root of 2 minus square root of 3 end fraction equals fraction numerator square root of 2 minus square root of 3 over denominator 2 minus 3 end fraction equals negative left parenthesis square root of 2 minus square root of 3 right parenthesis equals square root of 3 minus square root of 2 fraction numerator 1 over denominator square root of 3 plus square root of 4 end fraction cross times fraction numerator square root of 3 minus square root of 4 over denominator square root of 3 minus square root of 4 end fraction equals fraction numerator square root of 3 minus square root of 4 over denominator 3 minus 4 end fraction equals negative left parenthesis square root of 3 minus square root of 4 right parenthesis equals square root of 4 minus square root of 3 end style$

Sehingga

$begin mathsize 12px style fraction numerator 1 over denominator square root of 1 plus square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 plus square root of 3 end fraction plus fraction numerator 1 over denominator square root of 3 plus square root of 4 end fraction plus horizontal ellipsis plus fraction numerator 1 over denominator square root of 1.000.000 end root plus square root of 1.000.001 end root end fraction equals left parenthesis square root of 2 minus square root of 1 right parenthesis plus left parenthesis square root of 3 minus square root of 2 right parenthesis plus left parenthesis square root of 4 minus square root of 3 right parenthesis plus horizontal ellipsis plus left parenthesis square root of 1.000.0001 end root minus square root of 1.000.000 end root right parenthesis equals negative square root of 1 plus square root of 1.000.0001 end root equals square root of 1.000.0001 end root minus 1 end style$

Karena diketahui , maka nilai a - b = 1.000.001 - 1 = 1.000.000.

Jadi, jawaban yang tepat adalah B.