Study Space

Sum the following geometric series to infinity: 1/2+1/3^3+1/2^3+1/3^4+1/2^5+1/3^5+∞

Prove that the sum of n terms of the series: 11+103+1005+is10/9(10n−1)+n2.

Prove that : 61/2×61/4×61/8 _________ ∞=6.

Find the sum of the following series: (√2−1)+1+(√2−1)+∞

A person writes a letter to four of his friends. He asks each one of them to copy the letter and...

If S be the sum, P the product and R the sum of the reciprocals of n terms of a G.P, prove that...

Find the sum of the infinite geometric series (−5/4+5/16−5/64+...∞).

If f is a function satisfying f(x+y)=f(x)f(y) for all x,y∈N such that f(1)=3 and n∑x=1 f(x)=120...

Find the sum to n terms of the sequence (x+1/x)2,(x2+1/x2)2,(x2+1/x3)2,......

Find the sum to n terms of the sequence "an" given by an=2n+3n,nϵN.

Write the value of limx→0 sin5x / 2x

Find the equation of a line with slope -1 and cutting off an intercept of 4 units on negative.......

Find the equation of the line parallel to x-axis and passing through (3, -5).

Determine X so that the line passes through 3, 4 and X,5 Max 135 angle with the positive directio...

Find the angle between the lines joining the points (0, 0), (2, 3) and (2, −2), (3, 5).

Let A(6,4)andB(2,12) be two given points. Find the slope of a line perpendicular to AB.

Determine x so that 2 is the slope of the line (2,5) and (x,3).

What is the value of y so that the line through (3,y)and(2,7) is parallel to the line through (−1,..

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (- 1, - 1) are vert...

A quadrilateral has the vertices at the points (-4, 2), (2, 6), (8, 5) and (9, -7). Show that th....

Prove that (4,3) , (6,4) , (5,6) and (3,5) are the angular points of a square.

If the angle between two lines is π/4 and slope of one of the line is 1/2, find the slope of the...

Using the concept of slope, prove that medians of an equilateral triangle are perpendicular to the..

Prove that a triangle which has one of the angle as 30 degree, can not have all vertices with...

The vertices of a triangle are A(x1,x1tanθ1),B(x2,x2tanθ2) & C(x3,x3tanθ3). If the circumcentre...

Find the equation of a straight line cutting off an intercept-1 from the y-axis and being equally...

Find the equation of a straight line which makes an angle of Tan^-1 √2 with the -axis and cuts off..

Find the equation of a straight line which cuts off an intercept of length 3 on y - axis...

Find the equation of a line that has y-intercept as 4 and is perpendicular to line joining (2,−3)...

Find the equation of the straight line which makes an angles of 15∘ with the positive direction...