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The Persian mathematician Al-Karaji (953-1029) computed the first description of Pascal's triangle given below. It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048-1131); thus the triangle is also referred to as the Khayyam triangle in Iran.

The Persian mathematician Al-Karaji (953-1029) computed the first description of Pascal's triangle given below. It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048-1131); thus the triangle is also referred to as the Khayyam triangle in Iran.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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TASK 3 The Persian mathematician Al-Karaji (953-1029) computed the first description of Pascal's triangle given below. It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048-1131); thus the triangle is also referred to as the Khayyam triangle in Iran. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 15 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 The Pascal's triangle determines the coefficients which arise in binomial expressions. For example, consider the expansion (x + y)? = x² + 2xy + y = 1x³y® + 2x'y' + 1x®y?. The coefficients of the terms are in the third row of the triangle. As a general approach, In general, when x + y is raised to a positive integer power we have: (x + y)" = aox" + ax-ly + azx"-?y² + ... + an-1xy-1 + any", where the coefficients a; in this expansion are precisely the numbers on row (n+1) of Pascal's triangle. Each row of the triangle can be computed by adding the pairs of numbers in the previous row from left to right. Write, Compile and Execute a Java program that prints the Pascal's triangle given above.
Transcribed Image Text:TASK 3 The Persian mathematician Al-Karaji (953-1029) computed the first description of Pascal's triangle given below. It was later repeated by the Persian poet-astronomer-mathematician Omar Khayyám (1048-1131); thus the triangle is also referred to as the Khayyam triangle in Iran. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 15 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 The Pascal's triangle determines the coefficients which arise in binomial expressions. For example, consider the expansion (x + y)? = x² + 2xy + y = 1x³y® + 2x'y' + 1x®y?. The coefficients of the terms are in the third row of the triangle. As a general approach, In general, when x + y is raised to a positive integer power we have: (x + y)" = aox" + ax-ly + azx"-?y² + ... + an-1xy-1 + any", where the coefficients a; in this expansion are precisely the numbers on row (n+1) of Pascal's triangle. Each row of the triangle can be computed by adding the pairs of numbers in the previous row from left to right. Write, Compile and Execute a Java program that prints the Pascal's triangle given above.
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