Все публикации

0:03:22

Sum to n terms 1/(1.2.3) + 1/(2.3.4) + 1/(3.4.5) + ...

0:02:15

Find the sum to n terms: (1^2).2 + (2^2).3 + (3^2).4 + ...

0:03:45

Compute (x1)^2000 + (x2)^2000 where x1,x2 are roots of x^2 - x + 1 = 0.

0:04:20

Sum the series 1!/(a+1) + 2!/[(a+1)(a+2)] + ... + n!/[(a+1)(a+2) ... (a+n)].

0:04:24

Solve the equation sqrt(2x-1) + sqrt(3x-2) = sqrt(4x-3) + sqrt(5x-4).

0:01:54

Show that (a^2)[1+b^2] + (b^2)[1+c^2] + (c^2)[1+a^2] is greater than equal to 6abc.

0:03:43

Show that (A-C)(B-C)(A+D)(B+D) = q^2 - p^2 where A, B, C, D are defined as follows.

0:06:11

Show that roots of (1+z)^n = (1-z)^n are va;ues of i*tan(r*PI/n) where r = 0, 1, 2, .. (n-1).

0:02:34

Sum to n terms 1.(2^2) + 2.(3^2) + 3.(4^2) + ...

0:03:37

Sum to n terms 2.3 + 3.6 + 4.11 + ...

0:08:18

Prove that x^5-1 = (x-1)[square(x)+2xcos(PI/5)+1][square(x)-2xcos(2*PI/5)+1].

0:09:51

Prove |z1+z2+z3|^2+|-z1+z2+z3|^2+|z1-z2+z3|^2+|z1+z2-z3|^2=4[|z1|^2+|z2|^2+|z3|^2].

0:05:54

Compute 1 + i + square(i) + cube(i) + ... + i^n for n greater than equal to 1 where i = sqrt(-1).

0:07:06

Prove that |1+z1*conj(z2)|^2 + |z1-conj(z2)|^2 = [1+|z1|^2][1+|z2|^2].

0:06:06

Find the equation of circle whose radius and center are r and z0 respectively.

0:03:41

Prove that |1/z - 0.5| is less than 0.5 where Re(z) is greater than 1.

0:01:16

If A, B are imaginary cube roots of unity show that A^4 + B^4 + 1/(AB) = 0.

0:02:57

Sum to n terms: 2.1 + 5.3 + 8.5 + ...

0:09:25

Find the square of the distance of the point of intersection of the two given lines from the origin.

0:06:59

Transform the equation 17x^2-16xy+17y^2=225 to axes inclined at 45 degrees to original axes.

0:04:48

Solve z^4 = 5(z-1)[square(z)-z+1].

0:03:17

Find all quadratic equations one of whose roots is i^51+2i^80+3i^45+4i^38 where i=sqrt(-1).

0:01:46

Find all quadratic equations with real coefficients one of whose roots is (2+i)(3-i).

0:04:13

Factorize x^4 + 16 into linear polynomials.