(1/3)+(1/15)+(1/35)+...+((1/(2n-1)(2n+1))=n/2n+1
Matematika
iyan200
Pertanyaan
(1/3)+(1/15)+(1/35)+...+((1/(2n-1)(2n+1))=n/2n+1
1 Jawaban
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1. Jawaban yunzajauhari
cara 1
n= 1
1/ (2n-1)(2n-1) = n/ 2n+1
1/ (2(1)-1) (2(1)+1 = 1/ (2(1)+1)
1/ (1) (3) = 1/3
1/3 = 1/3 (benar)
cara 2
(k+1)
(1/3)+(1/15)+(1/35)+...+((1/(2n-1)(2n+1))=n/2n+1
(1/3)+(1/15)+(1/35)+...+((1/(2n-1)(2n+1)) + 1/ (2(k+1)-1) (2(k+1)+1) = (k+1) / (2(k+1)+1)
k/ (2k+1) + 1/ (2k+1) (2k+3) = k+1/ 2k+3
2k²+3k+1 / (2k+1) (2k+3) = k+1 / 2k+3
(2k+1) (k+1) / (2k+1)(2k+3) = k+1 / (2k+3)
k+1/ 2k+3 = k+1/ 2k+3 (benar)