I need to write a program to find the sum, sum of squares, sum of the cubes, and sum of a certain series shown below for the first n integers, begining with 1 and ending with n = 100.
Summing the first 100 natural numbers:
............... ............... ... n(n+1)
1 + 2 + 3 + ..... + n = ----------
............... ............... ......... 2
Sum of squares of the first 100 natural numbers:
............... ............... ........ n(n+1)(2n+1)
1² + 2² + 3² + ……. n² = -------------------
............... ............... ............... ..... 6
Sum of cubes of the first 100 natural numbers:
............... ............... ............... n² (n + 1)²
1³ + 2³ + 3³ + ……. + n³ = --------------
............... ............... ............... ..... 4
Another series:
...1........... 1............ 1.............. .......... 1.............. . n
------- + ------- + ---------- + .......... ---------- = .....--------
(1 * 2)... (2 * 3).... (3 * 4)............. . n*(n+1) ........... n +1
Since all of these series involve summing the same number of terms, do all of the summing inside ONE(1) loop. Compute the formats outside the loop. Use n as a variable in the formulas; do not replace it with 100, because the formulas work for any n and the program should be flexible enough to easily change the number of terms.
Summing the first 100 natural numbers:
............... ............... ... n(n+1)
1 + 2 + 3 + ..... + n = ----------
............... ............... ......... 2
Sum of squares of the first 100 natural numbers:
............... ............... ........ n(n+1)(2n+1)
1² + 2² + 3² + ……. n² = -------------------
............... ............... ............... ..... 6
Sum of cubes of the first 100 natural numbers:
............... ............... ............... n² (n + 1)²
1³ + 2³ + 3³ + ……. + n³ = --------------
............... ............... ............... ..... 4
Another series:
...1........... 1............ 1.............. .......... 1.............. . n
------- + ------- + ---------- + .......... ---------- = .....--------
(1 * 2)... (2 * 3).... (3 * 4)............. . n*(n+1) ........... n +1
Since all of these series involve summing the same number of terms, do all of the summing inside ONE(1) loop. Compute the formats outside the loop. Use n as a variable in the formulas; do not replace it with 100, because the formulas work for any n and the program should be flexible enough to easily change the number of terms.
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