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Home | 18.013A | Chapter 0 | Section 0.4 |
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Set this up on your own machine.
Solution:
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=-2 |
=A1+1 |
=B1+1 |
=C1+1 |
=D1+1 |
=E1+1 |
=F1+1 |
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=A1+1 |
1 |
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=A2+1 |
=C2*C$1+B2 |
=D2*D$1+C2 |
=E2*E$1+D2 |
=F2*F$1+E2 |
=G2*G$1+F2 |
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=A3+1 |
=C3*C$1+B3 |
=D3*D$1+C3 |
=E3*E$1+D3 |
=F3*F$1+E3 |
=G3*G$1+F3 |
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=A4+1 |
=C4*C$1+B4 |
=D4*D$1+C4 |
=E4*E$1+D4 |
=F4*F$1+E4 |
=G4*G$1+F4 |
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=A5+1 |
=C5*C$1+B5 |
=D5*D$1+C5 |
=E5*E$1+D5 |
=F5*F$1+E5 |
=G5*G$1+F5 |
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=A6+1 |
=C6*C$1+B6 |
=D6*D$1+C6 |
=E6*E$1+D6 |
=F6*F$1+E6 |
=G6*G$1+F6 |
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=A7+1 |
=C7*C$1+B7 |
=D7*D$1+C7 |
=E7*E$1+D7 |
=F7*F$1+E7 |
=G7*G$1+F7 |
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=A8+1 |
=C8*C$1+B8 |
=D8*D$1+C8 |
=E8*E$1+D8 |
=F8*F$1+E8 |
=G8*G$1+F8 |
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=A9+1 |
=C9*C$1+B9 |
=D9*D$1+C9 |
=E9*E$1+D9 |
=F9*F$1+E9 |
=G9*G$1+F9 |
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=A10+1 |
=C10*C$1+B10 |
=D10*D$1+C10 |
=E10*E$1+D10 |
=F10*F$1+E10 |
=G10*G$1+F10 |
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=A11+1 |
=C11*C$1+B11 |
=D11*D$1+C11 |
=E11*E$1+D11 |
=F11*F$1+E11 |
=G11*G$1+F11 |
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=A12+1 |
=C12*C$1+B12 |
=D12*D$1+C12 |
=E12*E$1+D12 |
=F12*F$1+E12 |
=G12*G$1+F12 |
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=A13+1 |
=C13*C$1+B13 |
=D13*D$1+C13 |
=E13*E$1+D13 |
=F13*F$1+E13 |
=G13*G$1+F13 |
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=A14+1 |
=C14*C$1+B14 |
=D14*D$1+C14 |
=E14*E$1+D14 |
=F14*F$1+E14 |
=G14*G$1+F14 |
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=A15+1 |
=C15*C$1+B15 |
=D15*D$1+C15 |
=E15*E$1+D15 |
=F15*F$1+E15 |
=G15*G$1+F15 |
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=A16+1 |
=C16*C$1+B16 |
=D16*D$1+C16 |
=E16*E$1+D16 |
=F16*F$1+E16 |
=G16*G$1+F16 |
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=A17+1 |
=C17*C$1+B17 |
=D17*D$1+C17 |
=E17*E$1+D17 |
=F17*F$1+E17 |
=G17*G$1+F17 |
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=A18+1 |
=C18*C$1+B18 |
=D18*D$1+C18 |
=E18*E$1+D18 |
=F18*F$1+E18 |
=G18*G$1+F18 |
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=A19+1 |
=C19*C$1+B19 |
=D19*D$1+C19 |
=E19*E$1+D19 |
=F19*F$1+E19 |
=G19*G$1+F19 |
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=A20+1 |
=C20*C$1+B20 |
=D20*D$1+C20 |
=E20*E$1+D20 |
=F20*F$1+E20 |
=G20*G$1+F20 |
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=C21*C$1+B21 |
=D21*D$1+C21 |
=E21*E$1+D21 |
=F21*F$1+E21 |
=G21*G$1+F21 |
which becomes
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-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
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-1 |
1 |
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0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
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|
1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
2 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
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|
3 |
0 |
1 |
3 |
1 |
0 |
0 |
0 |
0 |
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|
4 |
0 |
1 |
7 |
6 |
1 |
0 |
0 |
0 |
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5 |
0 |
1 |
15 |
25 |
10 |
1 |
0 |
0 |
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6 |
0 |
1 |
31 |
90 |
65 |
15 |
1 |
0 |
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7 |
0 |
1 |
63 |
301 |
350 |
140 |
21 |
1 |
|
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8 |
0 |
1 |
127 |
966 |
1701 |
1050 |
266 |
28 |
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9 |
0 |
1 |
255 |
3025 |
7770 |
6951 |
2646 |
462 |
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10 |
0 |
1 |
511 |
9330 |
34105 |
42525 |
22827 |
5880 |
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11 |
0 |
1 |
1023 |
28501 |
145750 |
246730 |
179487 |
63987 |
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12 |
0 |
1 |
2047 |
86526 |
611501 |
1379400 |
1323652 |
627396 |
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13 |
0 |
1 |
4095 |
261625 |
3E+06 |
7508501 |
9321312 |
5715424 |
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14 |
0 |
1 |
8191 |
788970 |
1E+07 |
40075035 |
63436373 |
49329280 |
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15 |
0 |
1 |
16383 |
2E+06 |
4E+07 |
2.11E+08 |
4.21E+08 |
408741333 |
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16 |
0 |
1 |
32767 |
7E+06 |
2E+08 |
1.1E+09 |
2.73E+09 |
3281882604 |
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17 |
0 |
1 |
65535 |
2E+07 |
7E+08 |
5.65E+09 |
1.75E+10 |
25708104786 |
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18 |
0 |
1 |
131071 |
6E+07 |
3E+09 |
2.9E+10 |
1.11E+11 |
1.97462E+11 |
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19 |
0 |
1 |
262143 |
2E+08 |
1E+10 |
1.48E+11 |
6.93E+11 |
1.49292E+12 |
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