STION 3 Obtain the four terms in the expansion of \( \left(1+\frac{x}{2}\right)^{10} \) in ascending powers of \( x \). Hence determine the approximation of \( (1.005)^{10} \) to 5 decimal places [10mark The sum of the first 8 terms of an AP is 12 and the sum of the first 16 terms is 56 , determine the first three terms of an AP. [5marks The 5th and 8th terms of a geometric progression are 80 and 640 respectively. Determine the values of the first term(a) and common ratio (r) [5marks
Added by Stephen C.
Close
Step 1
The Binomial Theorem states: \[ (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \] For \( \left(1+\frac{x}{2}\right)^{10} \), let \( a = 1 \) and \( b = \frac{x}{2} \). Show more…
Show all steps
Your feedback will help us improve your experience
Dr Harish Viswanathan and 66 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The sum to infinity of a geometric series is 96. The first term of the series is less than 30. The second term of the series is 18. (a) Find the first term and common ratio of the series. (5) (a) Show that the nth term of the series can be written as 3 * 2^(2n-5). (4) (b) Hence show that log(1) = (1 - 2log(2) + 5log(2)). (3)
Adi S.
Gregory H.
(a) Find the Maclaurin Series for arctan(x) (up to the term in x^5) by explicitly calculating the first five derivatives of arctan. (b) Now use the geometric series approach to find a power series for arctan(x). [We did this in class in Ex 3.6.] Check that you get the same result as in (a). 5. By any method find an expression for the sum of the infinite series: f(x) = sum(n=1 to inf) (x^(n+2))/(n(n+2)) = x^3/(1*3) + x^4/(2*4) + x^5/(3*5) + x^6/(4*6) + ... (-1 <= x <= 1) For any integrations you need to do you may use technology. 6. Use Taylor's inequality to decide how many terms of the series 1 + 1/(3*1!) + 1/(3^2*2!) + 1/(3^3*3!) + 1/(3^4*4!) + 1/(3^5*5!) + ... we need to take to approximate e^(1/3) to within 10^-8.
Keondre P.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD