<prompt> Tunafafanua misururu miwili ya vekta mathbfv_n na mathbfw_n kama ifuatavyo: Kwanza, mathbfv_0 anzapmatrix 1 3 endpmatrix, mathbfw_0 anzapmatrix 4 0 endpmatrix. Kisha kwa yote n ge 1, mathbfv_n ni makadirio ya mathbfw_n - 1 kwenye mathbfv_0, na mathbfw_n ni makadirio ya mathbfv_n kwenye mathbf w_0. Tafutamathbfv_1 mathbfv_2 mathbfv_3 dotsb.  <response>: Kwa kuwa mathbfv_n daima ni makadirio kwenye mathbfv_0,mathbfv_n a_n mathbfv_0kwa baadhi ya mara kwa mara a_n. Vile vile,mathbfw_n b_n mathbfw_0kwa b_n.asyukubwa wa kitengo 1.5 cm;jozi V, W;V0 1,3;W0 4,0;V1 W0 tafakari0,0,V0W02;W1 V1 tafakari0,0,W0V12;V2 W1 tafakari0,0,V0W12;W2 V2 tafakari0,0,W0V22;V3 W2 tafakari0,0,V0W22;W3 V3 tafakari0,0,W0V32;chora-1,0--5,0;chora0,-1--0,4;chora0,0--V0,nyekundu,Arrow6;chora0,0--W0,nyekundu,Arrow6;chora0,0--V1,nyekundu,Arrow6;chora0,0--W1,nyekundu,Arrow6;chora0,0--V2,nyekundu,Arrow6;chora0,0--W2,nyekundu,Arrow6;choraW0--V1--W1--V2--W2,iliyokatika;lebomathbfv_0, V0, NE;lebomathbfv_1, V1, NW;lebomathbfv_2, V2, NW;lebomathbfw_0, W0, S;lebomathbfw_1, W1, S;lebomathbfw_2, W2, S;asyKishaanzaalignmathbfv_n jina la kiendeshajiproj_mathbfv_0 mathbfw_n - 1 fracmathbfw_n - 1 cdot mathbfv_0mathbfv_02 mathbfv_0 fracb_n - 1 cdot mathbfw_0 cdot mathbfv_0mathbfv_02 mathbfv_0 fracb_n - 1 anzapmatrix 4 0 mwishopmatrix cdot anzapmatrix 1 3 mwishopmatrixleft anzapmatrix 1 3 mwishopmatrix kulia2 mathbfv_0 frac25 b_n - 1 mathbfv_0.endalignHivyo, a_n frac25 b_n - 1.Vile vile,anzaalignmathbfw_n jina la kiendeshajiproj_mathbfw_0 mathbfv_n fracmathbfv_n cdot mathbfw_0mathbfw_02 mathbfw_0 fraca_n cdot mathbfv_0 cdot mathbfw_0mathbfv_02 mathbfw_0 fraca_n anzapmatrix 1 3 mwishopmatrix cdot anzapmatrix 4 0 mwishopmatrixleft anzapmatrix 4 0 mwishopmatrix kulia2 mathbfw_0 frac14 a_n mathbfw_0.endalignHivyo, b_n frac14 a_n.Kwa kuwa b_0 1, a_1 frac25. Pia, kwa n ge 2,a_n frac25 b_n - 1 frac25 cdot frac14 a_n - 1 frac14 10 a_n - 1.Kwa hivyo, a_n ni mfuatano wa kijiometri yenye muhula wa kwanza frac25 na uwiano wa kawaida frac110, soanzaalignmathbfv_1 mathbfv_2 mathbfv_3 dotsb frac25 mathbfv_0 frac25 cdot frac110 cdot mathbfv_0 frac25 cdot left frac110 kulia2 cdot mathbfv_0 dotsb frac251 - 110 mathbfv_0 frac49 mathbfv_0 anzapmatrix 49 4 3 mwishopmatrix.mwishopanga 