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The greatest integer by which 1+sum(r=1)...

The greatest integer by which `1+sum_(r=1)^(30)rxxr !` is divisible is a. composite number b. odd number c. divisible by 3 d. none of these

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite t...

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  2. If bi=1-ai ,n a=sum(i=1)^n ai ,n b=sum(i=1)^n bi ,t h e nsum(i=1)^n ai...

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  3. The greatest integer by which 1+sum(r=1)^(30)rxxr ! is divisible is a....

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  4. (lim)(ntooo)sum(r=1)^n r/(1xx3xx5xx7xx9xxxx(2r+1)) is equal to 1/3 b. ...

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  5. Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal ...

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  6. If sum(r=1)^n r^4=I(n),t h e nsum(r=1)^n(2r-1)^4 is equal to a. I(2n)-...

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  7. If sum of an infinite G.P. : p ,1,1//p ,1//p^2, ........ is 9//2 then ...

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  8. The sum of i-2-3i+4 up to 100 terms, where i=sqrt(-1) is 50(1-i) b. 2...

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  9. If a1, a2, a3, ,a(2n+1) are in A.P., then (a(2n+1)-a1)/(a(2n+1)+a1)+(...

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  10. 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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  11. 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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  12. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

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

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

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  16. 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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  17. 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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  18. 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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  19. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

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

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