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Find the sum of the following series: `1/2+1/(3^2)+1/(2^3)+1/(3^4)+1/(2^5)+1/(3^6)+...+oo`

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Find the sum of n terms of the sequence (an),w h e r e an=5-6n ,n in ...

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  2. Show that the sequence loga ,log(a b),log(a b^2),log(a b^3), is an A.P...

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  3. Find the sum of the following series: 1/2+1/(3^2)+1/(2^3)+1/(3^4)+1/(...

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  4. Consider two A.P.: S2:2,7,12 ,17 , 500 terms a n dS1:1,8,15 ,22 , 300 ...

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  5. If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, the...

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  6. The sum of the first four terms of an A.P. is 56. The sum of the last ...

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  7. Given two A.P. 2,5,8,11...... T(60) and 3,5,7,9,......... T(50)dot Th...

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  8. In a certain A.P., 5 times the 5th term is equal to 8 times the 8th ...

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  9. Find the term of the series 25 ,22 3/4,20 1/2,18 1/4 which is numeric...

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  10. How many terms are there in the A.P. 3, 7, 11, ... 407?

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  11. If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

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  12. If (b+c-a)/a ,(c+a-b)/b ,(a+b-c)/c , are in A.P., prove that 1/a ,1/b ...

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  13. If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(1//a ...

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  14. Find the degree of the expression (1+x)(1+x^6)(1+x^(11))........(1+x^(...

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  15. In an A.P. of 99 terms, the sum of all the odd-numbered terms is 2550....

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  16. Divide 32 into four parts which are in A.P. such that the ratio of the...

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  17. Show (m+n)th and (m-n)t h terms of an A.P. is equal to twice the mth ...

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  18. If the sum of three consecutive numbers in A.P., is 24 and their pr...

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  19. Prove that the sum of n number of terms of two different A.P. s can be...

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  20. In an A.P. if S1=T1+T2+T3+.....+Tn (n is odd)S2=T2+T4+T6+.........+T(n...

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