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Pn= (1+x)(1-x2)(1+x3)....(1-x4n)/[(1+x)(1-x2)(1+x3)....(1-x2n)]2 Find lim(x→-1)Pn ...

Let f(x) be a real valued function not identically zero satisfies the equation, f(x+yn)=f(x)+(f(y))n for all real x & y and f'(0)≥0 where n(>1) is an odd natural number. Find f(10) ...

Find 1/2.4 + 1.3/2.4.6 + 1.3.5/2.4.6.8 +....till n terms ...

Find all numbers for which the product of all its factors (other than itself) is equal to the number itself. ...

can anyone express 179 in the given form- ab+ba.... condition- a and b are natural numbers...plzz...don't apply any complicated maths in it...do it in a simple way... thnks in advance for abiding the given conditions.... ...

Integration of Body = ?? ...

1/1.3 + 1/2.4 + 1/3.5 ... till infinite terms ...

f(x)=\begin{cases} 1-x & \text{ if } x<1 \\ (1-x)(2-x) & \text{ if } 1\leq x\leq 2 \\ 3-x & \text{ if } x>2 \end{cases} Determine the values of x for which the following function fails to be continuous or differentiable ...

(1), (2,3,4), (5,6,7,8,9),.... Find the sum of numbers in the nth group ...

Lim(x→∞)[ x2+1/x+1 -ax-b]=0 find a & b ...

1/1.2 + 1/2.3 + 1/3.4 +...till infinite ...

lim(n→∞) [ 2/π (n+1)cos-1( 1/n )-n] ...

a,b,c are in AP & a2,b2,c2 are in HP, then prove that a=b=c or a,b,-c/2 are in GP ...

If a, b, c be in GP & logca, logbc, logab be in AP, then prove that the common difference of AP is 3/2 ...

Lim(n→∞) 23-1/23+1 . 33-1/33+1 . 43-1/43+1 ... n3-1/n3+1 ...

lim(n→∞) 1/1+n2 + 2/2+n2 +...+ n/n+n2 ...

Find the summation s=x+x2+x4+x8.......till infinity ...

Consider a matrix whose entries are integers. Adding a same integer to all entries on a same row, or on a same column, is called an operation. It is given that, for infinitely many positive integers n , one can obtain, throug ...

Find f(5), given f'(x)=1+1/x and f(1)=1 ...

Find the lim(x→0) 1. [ Sinx/x ] 2. [sinx]/x 3. [lim(x→0) Sinx/x ] where [.] represents greatest integer function ...

Note: This is a question for people from classes 7 to 10 A Helium balloon is accelerating up (yes, we all know this is possible. So this is not a hypothetical situation but a practical one). So, note these things: 1) The ball ...

Let x,y,z be positive real numbers, satisfying the following inequality : (x+y+z)(\frac{1}{x}+ \frac{1}{y}+ \frac{1}{z}) < 10 Prove that x,y,z form sides of a triangle. If you know this , please don't post within a day. :) ...

Find all positive integers x and y satisfying the equation 3^x-2^y=7 ...

Show that out of {[x,2x,..,(n-1)x]} there must be one which differ from an integer by at most 1/n . Where x is a given real number and n is a given positive integer. ...

Find all real solutions to the system of equations: x+y=\sqrt{4z-1} ...(1) y+z=\sqrt{4x-1} ...(2) z+x=\sqrt{4z-1} ...(3) ...

Find the solutions to the system of equations in reals: x+\left \lfloor y \right \rfloor+\left \left \{ z\left. \right \} \right.=1.1 \left \lfloor x \right \rfloor+\left \{ y\left. \right \} \right.+z=2.2 \left \{ x\left. \r ...

1.Find all positive integers n, for which "2n+12n+2011n" is a perfect square. ...

A cylinder can move without friction along a straight wire parallel to its axis of symmetry, as shown. *Image* Tiny particles moving horizontally at speed v_0 bombard the body from both left and right. Collisions with the rig ...

A cylindrical tub contains water. We are only considering one axial plane of the cylinder (one that passes through the axis) The cylinder is now rotated about it's axis with constant angular velocity. Write the equation of th ...

1) n-factor is defined as: a) Number of moles of electrons either gained or lost per mole of reactant. b) Number of electrons either gained or lost per molecule of reactant. question: which is correct? A) a B) b C) both D) no ...