Chapter 3 Mathematica Mathematica e ( a n = ) n b n = n 1! + 1 2! n! b n a n e 3/n b n e 2/n! b n a n b n Mathematica Mat

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1 Chapter 3 Mathematica Mathematica e ( a n = ) n b n = n 1! + 1 2! n! b n a n e 3/n b n e 2/n! b n a n b n Mathematica Mathematica { }

2 26 3 {a, b, c} {{a, b}, {c, d}} {Sin[x], Cos[x], Tan[x]} [1] v1 v2 In[1]:= v1 = {a, b, c}; v2 = {p, q, r}; [2] v1 v2 In[2]:= v1 + v2 Out[2]= a p, b q, c r [3] In[3]:= 100*v1 Out[3]= 100a, 100b, 100c [4] 1 : In[4]:= v1 + 1 Out[4]= 1 a, 1 b, 1 c [5] x : In[5]:= x - v1 Out[5]= a x, b x, c x [6] 3 In[6]:= v1^3 Out[6]= a 3, b 3, c 3 [7] 5 In[7]:= 5^v1 Out[7]= 5 a, 5 b, 5 c [8] In[8]:= Exp[v1] Out[8]= a, b, c [9] In[9]:= v1^v2 Out[9]= a p, b q, c r [10] In[10]:= v1*v2 Out[10]= ap, bq, cr [11] In[11]:= v1/v2 Out[11]= a p, b q, c r

3 [12] In[12]:= v1.v2 Out[12]= ap bq cr 3.1 u = {1, 2, 3, 4, 5} x { 1 3 1, 2 3 2, 3 3 3, 4 3 4, }, { x, x 2 2!, x 3 3!, x 4 4!, x 5 } 5! n n! Factorial[n] u = {1, 2, 3, 4, 5}; 1 3 1, 2 3 2, 3 3 3, 4 3 4, 5 3 5, u^3 - u 0, 6, 24, 60, 120 x, x 2 /2, x 3 /3!, x 4 /4!, x 5 /5! u! 1, 2, 6, 24, 120 x^u/u! x, x2 2, x3 6, x4 24, x Range [13] Range {1, 2, 3, 4, 5} In[13]:= Out[13]= Range[5] 1, 2, 3, 4, 5 [14] Range {4, 5,..., 10} In[14]:= Range[4, 10] Out[14]= 4, 5, 6, 7, 8, 9, 10

4 28 3 [15] Range 4 x In[15]:= Range[4, 10, 0.7] Out[15]= 4., 4.7, 5.4, 6.1, 6.8, 7.5, 8.2, 8.9, Table [16] Table (square numbers) sq In[16]:= sq = Table[n^2, {n, 1, 10}] Out[16]= 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 Table[..] n n^2 Table [17] [[ ]] sq 7 In[17]:= sq[[7]] Out[17]= 49 [18] Length sq In[18]:= Length[sq] Out[18]= (e ) Table e a n = ( n ) n 10 N an [16] Table an = Table[N[(1 + 1/n)^n], {n, 1, 10}] 2., 2.25, , , , , , , , () Table x 1, x 2 1,, x 10 1 [16] Table x n 1

5 list = Table[x^n - 1, {n, 1, 10}] 1 x, 1 x 2, 1 x 3, 1 x 4, 1 x 5, 1 x 6, 1 x 7, 1 x 8, 1 x 9, 1 x 10 Factor list *1 Factor[list] 1 x, 1 x 1 x, 1 x 1 x x 2, 1 x 1 x 1 x 2, 1 x 1 x x 2 x 3 x 4, 1 x 1 x 1 x x 2 1 x x 2, 1 x 1 x x 2 x 3 x 4 x 5 x 6, 1 x 1 x 1 x 2 1 x 4, 1 x 1 x x 2 1 x 3 x 6, 1 x 1 x 1 x x 2 x 3 x 4 1 x x 2 x 3 x () mat = {m,a,t,h,e,m,a,t,i,c,a} tam Table (Hint tam n mat ) Reverse tam = Reverse[mat] Table mat len *2 mat = {m,a,t,h,e,m,a,t,i,c,a}; len = Length[mat]; tam n mat len - (n - 1) tam = Table[mat[[len - n + 1]], {n, 1, len}] a, c, i, t, a, m, e, h, t, a, m *1 Factor [8] Exp *2 len 11 Mathematica

6 30 3 [19] m1 *3 In[19]:= m1 = {{a, b, c}, {p, q, r}}; [20] MatrixForm m1 (matrix) In[20]:= Out[20]//MatrixForm= m1 //MatrixForm a b c p q r MatrixForm[m1] * 4*5 [19] m1 [21] TableForm m1 (table) In[21]:= m1 //TableForm Out[21]//TableForm= a b c p q r TableForm[m1] [22] Table In[22]:= m2 = Table[i + j, {i, 1, 4}, {j, 1, 5}] Out[22]= 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9 [23] TableForm In[23]:= m2 //TableForm Out[23]//TableForm= m2 [22] {i, 1, 4} {j, 1, 5} [24] [[ ]] 2 5 In[24]:= m2[[2, 5]] *3 [1] v1 = {a, b, c} v2 = {p, q, r} m1 = {v1, v2} *4 Sin[x] x//sin TableForm MatrixForm *5 MatrixForm 2*m1 2 2*MatrixForm[m1] TableForm

7 Out[24]= () TableForm Table kuku = Table[m * n, {m, 1, 9}, {n, 1, 9}]; kuku //TableForm Out[ ]//TableForm= kisuu = Table[(2 m - 1)*(2 n - 1), {m, 1, 10}, {n, 1, 10}]; kisuu //TableForm Out[ ]//TableForm= ( ) {n, n^2, n^3} power TableForm power = Table[{n, n^2, n^3}, {n, 1, 10}]; power //TableForm

8 32 3 Out[ ]//TableForm= Mathematica Sum [25] Sum In[25]:= Sum[n^2, {n, 1, 10}] Out[25]= n=1 n 2 [16] sq = Table[n^2, {n, 1, 10}] Table Sum [26] Mathematica 2 In[26]:= Out[26]= Sum[k^2, {k, 1, n}] 1 6 n 1 n 1 2n [27] 1 + 1/ /3 2 + In[27]:= Out[27]= Sum[1/n^2, {n, 1, Infinity}] Π 2 6 Infinity [28] 8 *6 In[28]:= Sum[x^n/n!, {n, 0, 8}] Out[28]= 1 x x2 2 x3 6 x4 24 x5 120 x6 720 x x *6 Sum[x^n/n!, {n, 0, Infinity}] Exp[x]

9 [29] Product n=1 (2n 1) In[29]:= Product[2*n - 1, {n, 1, 10}] Out[29]= [30] 3.5 In[30]:= Sum[m * n, {m, 1, 9}, {n, 1, 9}] Out[30]= ( ) e a n = ( ) n b n = n 1! + 1 2! n! (1) Sum b 5 (2) Table b n 10 bn (3) bn 3.2 an a n, a n e, b n, b n e x Abs[x] (1) N N[Sum[1/k!, {k, 0, 5}]] (2) Table N Sum bn = Table[ N[Sum[1/k!, {k, 0, n}]], {n, 1, 10}] 2., 2.5, , , , , , , , (3) an a 5 a 5 e an[[5]] Abs[an[[5]]-E] hikaku = Table[

10 34 3 {an[[n]], Abs[an[[n]]-E], bn[[n]], Abs[bn[[n]]-E]}, {n, 1, 10}]; hikaku //TableForm Out[ ]//TableForm= b n e b n Sum 3.8 () Mathematica (1). k + k 1 99 k=2 (2) , , ,... n 00 (3) m 1, 3, 5,..., 2m 1 2 m C 2 99 (1) 1 k + k 1 = k k 1 Mathematica Sum[3/(Sqrt[k] + Sqrt[k - 1]), {k, 2, 100}] N N *7 Sum[N[3/(Sqrt[k] + Sqrt[k - 1])], {k, 2, 100}] 27. (2) i *7 Sum[3.0/(Sqrt[k] + Sqrt[k - 1]), {k, 2, 100}]; 3 3.0

11 Sum[2/(i^2-1), {i, 2, n + 1}] 5n 3n n 2 n (3) mx (x x m ) 2 = (x x 2 m) + 2 x i x j 1 i<j m x i = 2i 1 (1 i m) Mathematica a = Sum[2 i - 1, {i, 1, m}]; b = Sum[(2 i - 1)^2, {i, 1, m}]; c = (a^2 - b)/2 1 2 m4 1 3 m 4m3 Factor[c] m m 1 m 3m2 3.5 Mathematica (1) i 1 m j 1 n i + j 1 i m,1 j n (i + j) (2) i, j, k 1 n i + j + k 1 i,j,k n (i + j + k) (3) 4 8 n S n S 99 S 100 S 1 S 100 S n 92 (Hint: S n 1 + log 10 S n x Floor[x] ) (4)

Chapter 3 Mathematica Mathematica e a n = ( ) n b n = n 1! + 1 2! n! b n a n e 3/n b n e 2/n! b n a n b n M athematica Ma

Mathematica Workbook Workbook Mathematica Mathematica A4 12 A5 9 14 4 2 Chapter 3 Mathematica Mathematica e a n = ( 1 + 1 ) n b n = 1 + 1 n 1! + 1 2! + + 1 n! b n a n e 3/n b n e 2/n! b n a n b n M athematica