Math Problem Statement
"Show that nP i=1 i3 = n(n+1) 2 2 using two methods. method 1 Use a telescoping sum as in class. method 2 Consider a square where each side has segments of length 1, 2, . . . , n; then the side length is 1 + 2 + · · · + n = n(n+1) 2 and the area of the square is A = n(n+1) 2 2 . Now consider areas a1, a2, . . . , an, where a1 is a unit square and a2, a3, . . . , an are as shown in the figure. Show that ai = i3 for i = 1, . . . , n. Hence the area of the square is also equal to A = a1 + a2 + · · · + an = nP i=1 ai = nP i=1 i3" can you do method 2
Solution
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Math Problem Analysis
Mathematical Concepts
Summation
Geometric interpretation
Formulas

Theorems

Suitable Grade Level
Advanced Mathematics