Find 1-7 + 4- ... 25 .+(-1)28128 ·

Name: Find 1-7 + 4- ... 25 .+(-1)28128 ·
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Description: Find 1-7 + 4- ... 25 .+(-1)28128 ·

The given series sum is 1-71+491-…+-128728128. The first term of the above series is 1 which can be…

Answered: + - ..+(-1)28 . ) 28_728 15

Math

Advanced Math

+ - ..+(-1)28 . ) 28_728 15

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter8: Roots And Radicals

Section8.8: Use The Complex Number System

Problem 8.156TI: Simplify: (a) (32i)+(54i) (b) (4+3i)(26i).

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Expert Solution

Step 1

The given series sum is $1 - \frac{7}{1} + \frac{49}{1} - \dots + {(- 1)}^{28} \frac{7^{28}}{1^{28}}$ .

The first term of the above series is 1 which can be considered as $1 = 7^{0}$ .

The second term is $- \frac{7}{1} = - 7$ .

The third term is $\frac{49}{1} = 7^{2}$ .

The fourth term would be $- \frac{343}{1} = - 7^{3}$ .

So, in general odd numbered terms have positive sign while even numbered term has negative sign.

The 29th term (odd numbered term) is ${(- 1)}^{28} \frac{7^{28}}{1^{28}} = 7^{28}$ .

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