Algebra questions | form five Pure Advanced Mathematics

(4020) Question Category: Mathematical Calculation

  1. Show that the term of sum_{r=1}^{n}ln2^{r} are in arithmetic progression. Find the sum of the first n terms .
  2. The third term of a convergent geometric progression is the arithmetic mean of the first and second terms. Find the common ratio and the sum  to infinity if the first term is 1.

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(4021) Question Category: Mathematical Calculation

  1. The sum of the first n terms of a series is (2^{n}-1). Find the general term of the series.
  2. Prove using Mathematical induction that 6^{n}+8^{n} is divisible by 7 for all positive odd numbers n.

Answer / Solution

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(4022) Question Category: Mathematical Calculation

  1. The sum to infinity of a geometric series whose second term is 4 is 16. Find
  1. The first term
  2. The common ratio
  1. i) Write the statement of the Maclaurin`s series for a function f(x) and use it to expand f(x)=(x+1)^{-1} up to the term x^{4}

         ii) Give the appropriate value of frac{5}{6} using the first 5 terms of the series in b(i) above correct to 4   decimal places.

Answer / Solution

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(4023) Question Category: Mathematical Calculation

  1. Show that the Newton Raphson Formula of finding the roots of the equation 12x^{3}+4x^{2}-15x-4=0 is x_{n+1}=frac{(24x_{n}+4)x_{n}^{2}+4}{(36x_{n}+8)x_{n}-15}  and use this formula to find the roots of  12x^{3}+4x^{2}-15x-4=0 correct to three decimal places.
  2. Approximate the area under the curve y=frac{1}{x-2} between x=2 and x=3 with six ordinates by :
  1. Trapesoidal rule
  2. Simpson rule
  1. Which among the rules in (b) above gives a better approximation to the area?.

Answer / Solution

UNSOLVED

(4109) Question Category: Mathematical Calculation

  1. Solve the equation small log _3 x-3+log_x 9=0
  2. The equations small x^{2}+9x+2=0 and small x^{2}+kx+5=0 have common roots. Find the quadratic equation giving two actual possible values of k.
  3. Find the sum of the series small frac{5}{1 imes 2 imes 3}+frac{8}{2 imes 3 imes 4}+frac{11}{3 imes 4 imes 5}+....frac{3n+2}{n(n+1)(n+2)}  hence find small sum_{r=1}^{alpha }frac{3r+2}{r(r+1)(r+2)}.
  4. If  small A=egin{bmatrix} 2 & 1&0 \ 1& 5&2 \ 1& -1 &1 end{bmatrix} and small B=egin{bmatrix} -1 & 2&0 \ 1& 3&2 \ 2& 0 &1 end{bmatrix}  Find the value of small A^{-1}B.

Answer / Solution

UNSOLVED

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