BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter F, Problem 40E
To determine

To show: The area of Gi=i3 and conclude that i=1ni3=[n(n+1)2]2.

Expert Solution

Explanation of Solution

The area of Gi is given by,

A=(k=1ik)2(k=1i1k)2=[i(i+1)2]2[i(i1)2]2=i24[(i+1)2(i1)2]=i24[(i+1+2i)(i2i+1)]

Simplify further as,

A=i24[i+1+2ii+2i1]=i24[4i]=i3

Hence, the area is proved.

Thus, from the given information, the area of ABCD is given by,

i=1ni3=[n(n+1)2]2.

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