## Question

###### If the sum of the coefficient of 1st ,2nd,3rd term of the expansion of (x2+1/x) raised to the power m is 46 then find the coefficient of the terms that does not contain x?

If the sum of the coefficient of 1st ,2nd,3rd term of the expansion of (x2+1/x) raised to the power m is 46 then find the coefficient of the terms that does not contain x?

## Answers

First find m.

## Explanation:

The first three coefficients will always be

#("_0^m ) = 1# ,#("_1^m ) = m# , and#("_2^m ) = (m(m-1))/2# .

The sum of these simplifies to

#m^2/2 + m/2 + 1# . Set this equal to 46, and solve for m.

#m^2/2 + m/2 + 1 = 46#

#m^2+ m + 2 = 92#

#m^2+ m - 90 = 0#

#(m + 10)(m - 9) = 0#

The only positive solution is#m = 9# .Now, in the expansion with m = 9, the term lacking x must be the term containing

#(x^2)^3(1/x)^6 = x^6/x^6 = 1#

This term has a coefficient of#("_6^9 ) = 84# .The solution is 84.

#### Similar Solved Questions

1 answers

##### Suppose ABC corp. is evaluating a project with the following incremental free-cash-flows (FCF) paid at the...

Suppose ABC corp. is evaluating a project with the following incremental free-cash-flows (FCF) paid at the end of the next four years. Which annual discount rate makes the NPV equal to zero? Enter your answer as a percent do not include the %. Round your final answer to two decimals. Timeline ...

1 answers

##### Please solve on paper and show the equation your gonna use 2. (30 pts) A small...

please solve on paper and show the equation your gonna use 2. (30 pts) A small disk of mass mi -0.75 kg is moving on a horizontal circle on a frictionless surface. The radius of the circle is 0.45 m. The block has a mass of m2 -1.7 kg and is stationary A) What is the tension in the string? B) Wha...

1 answers

##### The information below shows the cost for a year of college in public and private colleges...

The information below shows the cost for a year of college in public and private colleges in 2003-04 and 2014-15. What is the geometric mean annual increase for the period for the two types of colleges? (Round your answers to 2 decimal places.) Type of College 2003-04 2014-15 Public $ 3,120 ...

1 answers

##### C program Classwork_3.3: Correct the program below that will read two numbers: number of drinks and...

C program Classwork_3.3: Correct the program below that will read two numbers: number of drinks and number of sandwiches, and display the total bill calculated as: Total bill = Number of Drinks X 5.50 + Number of Sandwiches X 10.00 Answer the questions below. C-Program with error: Write the correct...

1 answers

##### 2. + 0/0.75 points Previous Answers SerCPWA11 1.WA.030. My Notes Ask Your Teacher The length of...

2. + 0/0.75 points Previous Answers SerCPWA11 1.WA.030. My Notes Ask Your Teacher The length of the slope of a mountain is 2520 m, and it makes an angle of 13.89 with the horizontal. What is the height of the mountain, relative to its base? 511.53 x m 3. + -10.75 points CJ10 1.P.038. My Notes Ask Yo...

1 answers

##### The following amounts (in thousands) were taken from the December 31 statements of financial position of...

The following amounts (in thousands) were taken from the December 31 statements of financial position of Maple Leaf Foods Inc.: 2015 2014 Total assets $2,630,865 $2,876,490 Total liabilities 577,731 631,994 How much is Maple Leaf Foods’ shareholders’ equity at Dece...

1 answers

##### Please answer all.... Thank you! 20.)The term spheroplast applies to a gram-negative bacterial cell which _____....

Please answer all.... Thank you! 20.)The term spheroplast applies to a gram-negative bacterial cell which _____. Select is likely to lyse due to the osmotic shock as your answer is likely to lyse due to the osmotic shock Select is just about to ready to produce a spore as your answer is jus...

1 answers

##### What is the largest carbon reservoir in the carbon cycle? A. forests B.grasses C.ocean D.microbes

what is the largest carbon reservoir in the carbon cycle? A. forests B.grasses C.ocean D.microbes...

1 answers

##### Please Show ALL Work 111. Use the guidelines to sketch the curve. 1. Find the domain...

Please Show ALL Work 111. Use the guidelines to sketch the curve. 1. Find the domain 11. Find Intercepts Symmetry (Even or Odd Function) iv. Asymptotes V. Increasing/Decreasing Intervals vi. Local Extrema Concavity and Inflection Points viii. Sketch the Graph with all above information vii. b) y ...

1 answers

##### Can you please write it down 300 or more words . I appreciate your help . nt LoraryBooksResourcesmailFacuity lexandr...

Can you please write it down 300 or more words . I appreciate your help . nt LoraryBooksResourcesmailFacuity lexandria School of Arts and Sciences 2018 OSTERM > Session C> 2018 OSTERM y Discussion Board hics rsity Discussion Time Now it is your turn. Martha needs help resolving her dilemma...

1 answers

##### с 11 a Solve the triangle. 35° А B 28 What is the length of side...

с 11 a Solve the triangle. 35° А B 28 What is the length of side a? a = (Round to the nearest whole number as needed.) What is the measure of angle B? B=0 (Round to the nearest degree as needed.) What is the measure of angle C? o (Round to the nearest degree as needed.)...

1 answers

##### The darkly pigmented end of a Xenopus (frog) egg is the ____________pole and will become the...

The darkly pigmented end of a Xenopus (frog) egg is the ____________pole and will become the future _ __________ of the frog O animal; anterior Odorsal; back Olateral; left side vegetal; anterior...

1 answers

##### Reduce the following reducible representation: D3d E 2C3 3C2 i 2S6 3σd ________________________________________________ r 7 1...

Reduce the following reducible representation: D3d E 2C3 3C2 i 2S6 3σd ________________________________________________ r 7 1 1 1 1 3...

1 answers

##### 31. On January 1, 2018, Huff Co. sold $5,000,000 of its 10% bonds for $4,426,480 to yield 12%. Interest is payable...

31. On January 1, 2018, Huff Co. sold $5,000,000 of its 10% bonds for $4,426,480 to yield 12%. Interest is payable semiannually on January 1 and July 1. What amount should Huff report as interest expense for the six months ended June 30, 2018? A) $221,330 B) $250,000 C) $265,589 D) $300,000...