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For the series, S=1+1/((1+3))(1+2)^2+1/(...

For the series, `S=1+1/((1+3))(1+2)^2+1/((1+3+5))(1+2+3)^2+1/((1+3+5+7))(1+2+3+4)^2` +... 7th term is 16 7th term is 18 Sum of first 10 terms is `(505)/4` Sum of first 10 terms is `(45)/4`

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a1, a2, a3, ,a(2n+1) are in A.P., then (a(2n+1)-a1)/(a(2n+1)+a1)+(...

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  2. If a 1 , a 2 , a 3 , , a 2 n + 1 are in A.P., then a 2 n + 1 − a 1 ...

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  3. For the series, S=1+1/((1+3))(1+2)^2+1/((1+3+5))(1+2+3)^2+1/((1+3+5+7)...

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  4. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

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  5. Let the terms a(1),a(2),a(3),…a(n) be in G.P. with common ratio r. Let...

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  6. IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...

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  7. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

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  8. Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(...

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  9. If l n(a+c),l n(a-c) and l n(a-2b+c) are in A.P., then (a) a ,b ,c ...

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  10. If a ,b ,a n dc are in G.P., then the equations a x^2+2b x+c=0a n ddx^...

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  11. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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  12. The third term of a geometric progression is 4. Then the product of t...

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  13. In triangle ABC medians AD and CE are drawn, if AD=5, angleDAC= pi/8 a...

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  14. Suppose a ,b, and c are in A.P. and a^2, b^2 and c^2 are in G.P. If...

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  15. If x ,y ,a n dz are pth, qth, and rth terms, respectively, of an A.P....

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  16. Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/...

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  17. If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a...

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  18. If a1, a2, a3, an are in H.P. and f(k)=(sum(r=1)^n ar)-ak ,t h e n (a...

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  19. If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P....

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  20. Let a+a r1+a r1 2++ooa n da+a r2+a r2 2++oo be two infinite series of ...

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