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Single Variable Calculus: Early Tr...

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

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BuyFindarrow_forward

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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Chapter E Solutions

Single Variable Calculus: Early Transcendentals
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Ch. E - Write the sum in sigma notation. 11. 1+2+3+4++10Ch. E - Write the sum in sigma notation. 12. 3+4+5+6+7Ch. E - Write the sum in sigma notation. 13....Ch. E - Write the sum in sigma notation. 14....Ch. E - Write the sum in sigma notation. 15. 2+4+6+8++2nCh. E - Write the sum in sigma notation. 16....Ch. E - Write the sum in sigma notation. 17. 1 + 2 + 4 + 8...Ch. E - Write the sum in sigma notation. 18....Ch. E - Write the sum in sigma notation. 19. x+x2+x3++xnCh. E - Write the sum in sigma notation. 20....Ch. E - Find the value of the sum. 21. i=48(3i2)Ch. E - Find the value of the sum. 22. i=36i(i+2)Ch. E - Find the value of the sum. 23. j=163j+1Ch. E - Find the value of the sum. 24. k=08coskCh. E - Find the value of the sum. 25. n=120(1)nCh. E - Find the value of the sum. 26. i=11004Ch. E - Find the value of the sum. 27. i=04(2i+i2)Ch. E - Find the value of the sum. 28. i=2423iCh. E - Find the value of the sum. 29. i=1n2iCh. E - Find the value of the sum. 30. i=1n(25i)Ch. E - Find the value of the sum. 31. i=1n(i2+3i+4)Ch. E - Find the value of the sum. 32. i=1n(3+2i)2Ch. E - Find the value of the sum. 33. i=1n(i+1)(i+2)Ch. E - Find the value of the sum. 34. i=1ni(i+1)(i+2)Ch. E - Find the value of the sum. 35. i=1n(i3i2)Ch. E - Find the number n such that i=1ni=78.Ch. E - Prove formula (b) of Theorem 3.Ch. E - Prove formula (e) of Theorem 3 using mathematical...Ch. E - Prove formula (e) of Theorem 3 using a method...Ch. E - Prove formula (e) of Theorem 3 using the following...Ch. E - Evaluate each telescoping sum. (a) i=1n[i4(i1)4]...Ch. E - Prove the generalized triangle inequality:...Ch. E - Find the limit. 43. limni=1n1n(in)2Ch. E - Find the limit. 44. limni=1n1n[(in)3+1]Ch. E - Find the limit. 45. limni=1n2n[(2in)3+5(2in)]Ch. E - Find the limit. 46. limni=1n3n[(1+3in)32(1+3in)]Ch. E - Prove the formula for the sum of a finite...Ch. E - Evaluate i=1n32i1.Ch. E - Evaluate i=1n(2i+2i).Ch. E - Evaluate i=1m[j=1n(i+j)].

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