A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- STATEMENT -1: (666...n digit)^2+(888... ndigit)=(444....2ndigits) STAT...
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- Let a1,a2,a3,.... are in GP. If an>am when n>m and a1+an=66 while a2*a...
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- Find the sum of 2n terms of the series whose every even term is ' a ' ...
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- If the sum of an infinite G.P is 32 and the some of its first two term...
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- If Sn=1+r^n+r^(2n)+r^(3n)+.... to oo and sn=1-r^n+r^(2n)-r^(3n)+... to...
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- If x=sum(n=0)^oo a^n, y=sum(n=0)^oo b^n where |a|<1,|b|<1 then prove t...
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- If exp. {(sin^2x+sin^4x+sin^6x+…inf.) In2} satisfies the equation x^2-...
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- If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...
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- If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...
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- If S1, S2,S3,S4,.....,Sp denotes the sums of infinite geometric serie...
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- If a,b,c are in G.P., then show that : loga, logb, log c are in A.P.
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- If a,b,c are in A.P. and x,y,z in G.P., prove that x^(b-c).y^(c-a).z^(...
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- If a, b, c are in A.P and a, b, d are in G.P, prove that a, a -b, d ...
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- 29. If a,b,c are in G.P. and a^(1/x)=b^(1/y)=c^(1/z) prove that x, y, ...
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- If a, x, b as well as c, x, d are in GP while a^2,y,b^2 as well as c^2...
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- If pth, qth and rth terms of an A.P. and G.JP. Both be a,b and c respe...
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- If pth, qth , rth and sth terms of an AP are in GP then show that (p-q...
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- If second third and sixth terms of an A.P. are consecutive terms o a ...
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- Find an AP of distinct terms whose first term is unity such that the s...
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- In a set of four number, the first three are in GP & the last three ar...
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