A DAS GUPTA-Progression, Related Inequalities and Series-Exercise
- Show that (n-1)/(n+1)+3((n-1)/(n+1))^2+5((n-1)/(n+1))^3+....+oo=sum(r=...
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- Find the sum to n terms of the series 1*2^2 + 2*3^2 + 3*4^2 + ...
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- (x^2+1/(x^2)+2)+(x^4+1/(x^4)+5)+(x^6+1/(x^6)+8)+
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- Sum to infinite terms : 1/5-2/7^2+3/5^3-4/7^4+....
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- Sum to n terms : 0.4+0.44+0.444+....
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- Find the sum to n terms of the series 5 + 55 + 555 + ...
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- Natural numbers are divided into groups in the following way: 1,(2,3),...
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- Prove that the sum of the numbers in any group in the following is the...
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- Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...
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- Sum to n terms of the series (1)/((1+x)(1+2x))+(1)/((1+2x)(1+3x))+(1)/...
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- The sum of the series : 1/(1*2*3*4)+1/(3*4*5*6)+1/(5*6*7*8)+...+oo is
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- Sum to n terms of the series 1/(5!)+1/(6!)+(2!)/(7!)+(3!)/(8!)+.........
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- ((1)/(x+1)+(1)/(x+5))=((1)/(x+2)+(1)/(x+4)):
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- Evaluate sum(n=1)^n (n^2+n-1)/((n+2)!).
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- Evaluate sum(r=1)^n (rr!) =
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- If a1,a2,a3,...,an are in AP and ai ne (2k-1)pi/2 for all i, find the ...
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- Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+ is equal...
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- Sum of infinite series 1/(1*4)+1/(4*7)+1/(7*10)+......oo is
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- If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...
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- "If " (a^(n)+b^(n))/(a^(n-1)+b^(n-1))" is the A.M. between" a and b, t...
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