Sequence and Series questions
1035 published questions with worked solutions.
- The sum of the series 1 1+ 2 + 1 2+ 3 + 1 3+ 4 + + 1 n^2-1 + n^2 equals
- The fourth, seventh and tenth terms of a G.P. are p,q and r respectively, then
- If S denotes the sum to infinity and S_n the sum of n terms of the series 1+ 12+ 14+ 18+ , such that S-S_n< 1 1000 , then the...
- If the sum of the series 2,5,8,11, is 60100, then n, the number of terms, is
- After inserting n A.Ms between 2 and 38, the sum of the resulting progression is 200. The value of n is
- The cubes of the natural numbers are grouped as 1^3, (2^3,3^3 ), (4^3,5^3,6^3 ), , then the sum of the numbers in the n^ th group...
- The sum of 11 terms of an A.P. whose middle term is 30, is
- _ n=0 ^ ( _ex)^n n! is equal to
- The sum of the series 1^2 2^2 1! + 2^2 3^2 2! + 3^2 4^2 3! + , is
- If S_n denotes the sum of the products of the first n numbers taken two at a time, then _ n=0 ^ S_n (n+1)! equals
- The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its...
- Suppose that all the terms of an arithmetic progression are natural numbers. If the ratio of the sum of the first seven terms to...
- Let S_k, where k=1,2, ,100, denotes the sum of the infinite geometric series whose first term is k-1 k! and the common ratio is...
- Let a,b,c be positive integers such that ba is an integer. If a,b,c are in geometric progression and the arithmetic mean of a,b,c...
- A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers...
- Let a_1,a_2,a_3, ,a_ 11 be real numbers satisfying a_1=15, 27>2a_2>0 and a_k=2a_ k-1 -a_ k-2 for k=3,4, ,11. If a_1^2+a_2^2+ +a_...
- Let a_1,a_2,a_3, ,a_ 100 be an arithmetic progression with a_1=3 and S_p= _ i=1 ^pa_i, 1 p 100. For any integer n with 1 n 20,...
- If x_1,x_2, ,x_n are any real numbers and n is any positive integer, then
- Let b_i>1 for i=1,2, ,101. Suppose _eb_1, _eb_2, , _eb_ 101 are in Arithmetic Progression (A.P.) with the common difference _e2....
- If the 2^ nd , 5^ th and 9^ th terms of a non-constant AP are in GP, then the common ratio of this GP is
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