A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- "If "a1,a2,a3,.....,an" are in AP, prove that "a(1)+a(n)=a(r)+a(n-r+1)...
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- If a1,a2,a3,.....,an are in AP, prove that 1/(a1a2)+1/(a2a3)+1/(a3a4)+...
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- If a1,a2,a3,………an are in A.P, where ai.0 for all i show that 1/(sqrt(a...
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- Let a1,a2,a3 …. an be in A.P. If 1/(a1an)+1/(a2a(n-1))+… + 1/(an a...
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- If the sequence a(1),a(2),a(3),…,a(n) is an A.P., then prove that a(1)...
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- If the nonzero numbers a1,a2,a3,....,an are in AP, prove that 1/(a1a2a...
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- If a,b,c are in A.P. prove that b+c,c+a,a+b are also in A.P.
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- If ab+bc+ca!=0 and a,b,c are in A.P. prove that a^2(b+c), b^2(c+a), c^...
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- If a^2,b^2,c^2 are in A.P. prove that 1/(b+c),1/(c+a),1/(a+b) are in A...
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- If a^2, b^2, c^2 are in A.P, show that: a/(b+c), b/(c+a), c/(a+b) are...
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- If x, y, z are in AP, prove that 1/(sqrty+sqrtz),1/(sqrtz+sqrtx),1/(sq...
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- If Sn=an^2+bn+c where c ne 0 and Sn denotes the sum to n terms of a se...
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- The sum of n terms of a series is 2n^2+3n. Is the series arithmetic ? ...
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- Find the sum of all positive integers less than 200 that are divisible...
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- Find the sum of all natural numbers n in [100, 300] that are neither d...
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- Find the sum of all 3-digit natural numbers which are of the form 3m+2...
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- Sum the series to n terms: 1/(1+sqrtx)+1/(1-x)+1/(1-sqrtx)+.....
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- How many terms of 1+3+5+7+... amount to 1234321 ?
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- The maximum sum of the series 20+19 1/3+18 2/3+ is 310 b. 300 c. 0320 ...
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- If a1,a2...................,a19 are the first 19 term of an AP and a1+...
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