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If n >1 , the value of the positive inte...

If `n >1` , the value of the positive integer `m` for which `n^m+1` divides `a=1+n+n^2+ddot+n^(63)` is/are `8` b. `16` c. `32` d. `64`

A

8

B

16

C

32

D

64

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`a=(n^(64)-1)/(n-1)`
`=(n+1)(n^(2)+1)(n^(4)+1)(n^(8)+1)(n^(16)+1)(n^(32)+1)`
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CENGAGE-PROGRESSION AND SERIES-Exercise (Multiple & Comprehension)
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  7. If a, b and c are in G.P and x and y, respectively , be arithmetic mea...

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  8. Consider a sequence {an} with a1=2 & an =(a(n-1)^2)/(a(n-2)) for all ...

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  10. The sum of an infinite geometric series is 162 and the sum of its firs...

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  11. If 1/a,1/b,1/c are in A.P and a,b -2c, are in G.P where a,b,c are non-...

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  12. Sum of an infinite G.P is 2 and sum of its two terms is 1.If its secon...

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  13. For 0 lt phi lt pi//2 , if x =Sigma(n=0)^(oo) cos^(2n) phi ,y=Sigma(n...

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  14. 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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  15. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then a. a-b=d-c ...

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  16. If Sn=1^2-2^2+3^2-4^2+5^2-6^2+...... ,t h e n

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  17. 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+ n terms ...

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  18. If vec a= hat i+2 hat j+3 hat k and vec b=2 hat i+4 hat j−5 hat k rep...

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  19. Given that x+y+z =15 when a,x,y,z,b are in A.P and 1/x+1/y+1/z=5/3 whe...

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  20. If a, b and c are in H.P., then the value of ((ac+ab-bc)(ab+bc-ac))/(a...

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