Sequence and Series questions
1035 published questions with worked solutions.
- The sum of 0.2+0.004+0.00006+0.0000008+ to is
- _ r=1 ^n r^2- _ m=1 ^n _ r=1 ^m r is equal to
- If _ n=1 ^n n, 10 3 _ n=1 ^n n^2, _ n=1 ^n n^3 are in GP then the value of n is
- The value of _ r=1 ^ n (2r-1)a+ 1 b^ r is equal to
- If s_n= _ n=1 ^ n 1+2+2^ 2 + to n terms 2^ n then s_n is equal to
- Let S_n denote the sum of the cubes of the first n natural numbers and s_n denote the sum of the first n natural numbers. Then _...
- If in a series t_n= n (n+1)! then _ n=1 ^ 20 t_n is equal to
- If t_n denotes the nth term of the series 2+3+6+11+18+ then t_ 50 is
- The sum of n terms of the series 1^ 2 +2 2^ 2 +3^ 2 +2 4^ 2 +5^ 2 +2 6^ 2 + is n(n+1)^ 2 2 when n is even. When n is odd, the sum...
- Observe that 1^ 3 =1, 2^ 3 =3+5, 3^ 3 =7+9+11, 4^ 3 =13+15+17+19. Then n^ 3 as a similar series is
- Let t_r=2^ r/2 +2^ -r/2 . Then _ r=1 ^ 10 t_r^ 2 is equal to
- The sum of 3 1 2 12+ 4 2 3 ( 12 )^ 2 + 5 3 4 ( 12 )^ 3 + to n terms is equal to
- Let f(n)= [ 12+ n 100 ] where [x] denotes the integral part of x. Then the value of _ n=1 ^ 100 f(n) is
- A_r; r=1,2,3, ,n are n points on the parabola y^ 2 =4x in the first quadrant. If A_r=(x_r,y_r), where x_1,x_2,x_3, ,x_n are in GP...
- The lengths of three unequal edges of a rectangular solid block are in GP. The volume of the block is 216 cm ^ 3 and the total...
- If AM of the numbers 5^ 1+x and 5^ 1-x is 13 then the set of possible real values of x is
- If the AM of two positive numbers be three times their geometric mean then the ratio of the numbers is
- If a,b,c are in HP then 1 b-a + 1 b-c is equal to
- S_r denotes the sum of the first r terms of an AP. Then S_ 3n :(S_ 2n -S_n) is
- The value of _ r=1 ^ n 1 a+rx + a+(r-1)x is
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