Text Solution
AI Generated Solution
A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- If ai>0,i=1,2,3,...n and (n-1)s=a1+a2+a3+....+an, prove that a1*a2*a3*...
Text Solution
|
- If 2a+b+3c=1 and a gt 0, b gt 0, c gt 0 , then the greatest value of ...
Text Solution
|
- Given the perimeter of a triangle, prove that the triangle of the grea...
Text Solution
|
- Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+,...
Text Solution
|
- Find the sum of first n terms of the series 0.7 + 0.77 + 0.777 + …..
Text Solution
|
- The sum of the series 3/(1^2)+5/(1^2+2^2)+7/(1^2+2^2+3^2)+..... upto n...
Text Solution
|
- If a1,a2,a3,.....,an are in AP where ai ne kpi for all i, prove that c...
Text Solution
|
- Find the sum of the series cot^(-1) 7+cot^(-1)13+cot^(-1)21+cot^(-1)...
Text Solution
|
- The coefficient of x^98 in the expression of (x-1)(x-2)......... (x -...
Text Solution
|
- If m times the mth term of an AP is equal to n times its nth term, the...
Text Solution
|
- Prove that the numbers sqrt2,sqrt3,sqrt5 cannot be three terms (not ne...
Text Solution
|
- If a, b and c are three terms of an A.P. such that a !=b, then (b-c)/(...
Text Solution
|
- If loglx,logmx,lognx are in AP where x ne 1 and x is positive, prove t...
Text Solution
|
- If log3 2, log3 (2^x -5) and log3 (2^x-7/2) are in A.P, determine the ...
Text Solution
|
- If the triplets log a, log b, log c and (log a-log 2b), (log 2b-log 3c...
Text Solution
|
- Find three-digit numbers that are divisible by 5 as well as 9 and whos...
Text Solution
|
- 1000 ! Is divisible by 10^n. Find the largest positive integral value ...
Text Solution
|
- Find the number of common terms in the following sequences : 3, 7, 11,...
Text Solution
|
- Find the number of common terms in the following sequences : 1, 5, 9, ...
Text Solution
|
- Find the four numbers in A.P., whose sum is 50 and in which the gre...
Text Solution
|