Download Problem #1: Sum of reciprocals of odd integers from 3 to 63 Problem

Section A
Ritvik Rao
11/23/2016
Problem #1: Sum of reciprocals of odd integers from 3 to 63
Sum1  2 * i + 1, {i, 1, 31}
31 674 468 729 962 723 297 623 231
18 472 920 064 106 597 929 865 025
Problem #2: Sum of 1/(1+1/(1+1/(1+1/2)))
1  1 + 1  1 + 1  1 + 1  2
5
8
Problem #3: Pi to 50 digits
N[Pi, 50]
3.1415926535897932384626433832795028841971693993751
Problem #4: 1000th prime
Prime[1000]
7919
Problem #5: sin x, sin 2x, and sin 3x on the same graph
Plot[{Sin[x], Sin[2 x], Sin[3 x]}, {x, 0, 2 Pi},
AxesLabel → {x, y}, PlotLegends → "Expressions"]
y
1.0
0.5
sin(x)
1
2
3
4
5
6
x
sin(2 x)
sin(3 x)
-0.5
-1.0
Problem #6: Prime factorization of 2,381,400
FactorInteger[2 381 400]
{{2, 3}, {3, 5}, {5, 2}, {7, 2}}
Above, the results are interpreted as follows: For each pair of numbers in the bracket, the first number is
the factor value, and the second number is the exponent. For example, {2,3} means 2^3.
Problem #7: Solving 2^x=100
N[Log[2, 100]]
6.64386
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Section A
Ritvik Rao
11/23/2016
NSolve[2 ^ x ⩵ 100, x, Reals]
{{x → 6.64386}}
Problem #8: 115th and 1,115th Fibonacci number
Fibonacci[115]
483 162 952 612 010 163 284 885
Fibonacci[1115]
46 960 625 891 577 894 920 915 085 010 622 289 470 462 518 359 149 677 075 881 383 631 822 660 890 718 642 
869 603 700 018 836 567 361 824 279 444 479 341 088 310 462 978 732 670 769 895 389 845 153 583 927 059 
046 832 024 176 024 794 070 671 098 298 816 588 315 827 802 770 672 734 166 457 585 412 100 971 385
Problem #9: GCD and LCM of 5335 and 40425
GCD[5335, 40 425]
55
LCM[5335, 40 425]
3 921 225
Problem #10: Sum of squares of first 20 integers
Sum[i ^ 2, {i, 1, 20}]
2870
Total[{1 ^ 2, 2 ^ 2, 3 ^ 2, 4 ^ 2, 5 ^ 2, 6 ^ 2, 7 ^ 2, 8 ^ 2, 9 ^ 2, 10 ^ 2,
11 ^ 2, 12 ^ 2, 13 ^ 2, 14 ^ 2, 15 ^ 2, 16 ^ 2, 17 ^ 2, 18 ^ 2, 19 ^ 2, 20 ^ 2}]
2870
Problem #11: Sum of reciprocals of odd integers from 15 to 51
Sum1  2 * i + 1, {i, 7, 25}
63 501 391 475 806 044 193
96 845 140 757 687 397 075
Problem #12: Value of (1/1+1/2+1/3+1/4)+(2/1+2/2+2/3+2/4)+(3/1+3/2+3/3+3/4)
Sum1 + 2 + 3  i, {i, 1, 4}
25
2
Sum1  i, {i, 1, 4} + Sum2  i, {i, 1, 4} + Sum3  i, {i, 1, 4}
25
2
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