Frequent Progressions Questions

Find the sum of n terms and Sum to infinite terms of the Series - 1/4 + 1.3/4.6 + 1.3.5/4.6.8 + 1.3.5.7/4.6.8.10 +............. ...

12+14+24+58+164+........+n=????? The answer is 3n-n2+11n-1 Please someone show me the way to solve it. ...

The ratio of A.M. (arithmetic mean) and G.M. (geometric mean) of two positive number a and b is m:n. Prove that a:b = (m2 + m2 - n2 ):(m2 - m2 - n2 ...

If x2-x+1=0 and the two roots of the equation are α and β;then find the value of α2013+β2013. ...

if a x x x x b x x = f(x)-xf/(x). x x c x x x x d then f(x)=? ...

If a) x1 + x2 + ...................+x1007 =(2014)2 b) x1 /(x1 +1)=x2 /(x2 +3)=.....................=x1007 /(x1007 +2013) then x253 =? ...

Find the numebr of solutions of the equation- 8[x2 - x] + 4[x]=13+12[sinx],where [.]denotes the G.I.F. ...

Please post a brief soln to the problem 1) The no. of right triangles with integer sides and inradius r=2013 2)Let a,b,c,d be non zero digits. If n is the no. of 4 digit no.s abcd such that ab+cd is even, then last digit of n ...

For x ≥ 0, the smallest value of the function f(x) = 4x2+8x +13/ 6(x+1) is : ...

If S(n) = Σnk=1 4 k /4 k 4 + 1 then find the value of 221s(10)/10 lz show the ful sonn... ...

Out of (2n+1) tickets numbered consecutively, three are drawn at random. the chance that the numbers on them are in A.P is (a) n2/4n2-1 (b) 2n/4n2-1 (c) 3n/4n2-1 (d) 4n/4n2-1 ...

If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum possible value of b is (a) 23/2 (b) 22/3 (c)21/3 (d) 25/2 ...

P.t. (1+x)3/4+( 1+5x) /(1-x)2 = 2+ 29/4 x + 297/32 x2(nearly ...) ...

10 DISTINCT alphabetas are given. 5 letter words are to be formed . no. of ways in which at least one allphabet is repeated . is : ...

The value of the expression 47C4 + j=15Σ52-j C3 IS ... ...

Find the H.C.F. of the minimum non-negative values of a,b and c, given that the equation x4+ax3+bx2+cx+1=0 has only real; roots ... ...

The product of n positive numbers is unity.Then their sum is a.a positive integer b.divisible by n c.equal to n + 1/n d.never less than n Let the numbers be a1,a2,a3.......an Applying A.M>=G.M we get, a1+a2+a3+............ ...

If a,b,c are in AP ;b,c,a In GP then prove that 1/c , 1/a , 1/b are in ap ...

Find till infinity: 1 - n^2 + {n^2(n^2-1^2)}/(2!)^2 - {n^2(n^2-1^2)(n^2-2^2)}/(3!)^2................................ to infinity,where n belongs to N. ...

The maximum value M of 3x+5x-9x+15x-25x,as x varies over reals,satisfies A.3<M<5 B.9<M<25 C.0<M<2 D.5<M<9 ...

S=1-1+1-1+1-1....................... infinity now thus, S=1- (1-1+1-1+1-1....................... infinity) thus S=1-S thus 2S=1 S=1/2 ...

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