   # Find the number n such that ∑ i = 1 n i = 78 . ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305270336

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305270336
Chapter E, Problem 36E
Textbook Problem
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## Find the number n such that ∑ i = 1 n i = 78 .

To determine

To find: The number n such that i=1ni=78.

### Explanation of Solution

Theorem used:

Let c be a constant and n be a positive integer. Then,

i=1nc=nc, i=1ni=n(n+1)2 and i=1ni2=n(n+1)(2n+1)6.

Calculation:

By the above theorem, it is given that i=1ni=n(n+1)2.

Thus, the expression i=1ni=78 simplified as, n(n+1)2=78.

Solve the equation n(n+1)2=78 and obtain the value of n.

n(n+1)2=78n(n+1)=156n2+n156=0

The equation n2+n156=0 is a quadratic equation with variable n

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