(2³-1)(3³-1)...(100³-1)/(2³+1)(3³+1)...(100³+1)=A/B. Nilai dari B-A adalah... a. 5050 b. 3637 c. 2413 d. 1683 e. 1413

menggunakan sifat
p^3 + q^3 = (p + q)(p^2 - pq + q^2)
dan
p^3 - q^3 = (p - q)(p^2 + pq + q^2)

(2^3 - 1)(3^3 - 1)...(100^3 - 1) / (2^3 + 1)(3^3 + 1)...(100^3 +1)
= (2 - 1)(2^2 + 2.1 + 1^2)(3 - 1)(3^2 + 3.1 + 1^2)...(100 - 1)(100^2 + 100.1 +1) / (2 + 1)(2^2 - 2.1 + 1^2)(3+1)(3^2 - 3.1 + 1^2)...(100 + 1)(100^2 - 100.1 + 1)

= (1)(4 + 2 + 1)(2)(9 + 3 + 1)...(99)(10000 + 100 + 1) / (3)(4 - 2 + 1)(4)(9 - 3 + 1)...(101)(10000 - 100 + 1)

= (1)(7)(2)(13)...(99)(10101) / (3)(3)(4)(7)...(101)(9901)

= (1.2.3.4....99)(7.13.21.31.....10101) / (3.4.5.6....101)(3.7.13.21.....9901)

= (1.2)(10101) / (100 . 101)(3)

= 20202 / 30300

= 3367 / 5050

A = 3367
B = 5050

B - A = 5050 - 3367 = 1683
**D**