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The sum of first 20 terms of the sequenc...

The sum of first 20 terms of the sequence `0.7,0.77,0.777,"……"` is

A

`(7)/(9)(99-10^(-20))`

B

`(7)/(81)(179+10^(-20))`

C

`(7)/(9)(99+10^(-20))`

D

`(7)/(81)(179-10^(-20))`

Text Solution

Verified by Experts

The correct Answer is:
B
`S=0.7+0.77+0.777+"......."" upto 20 terms "`
`=(7)/(9)(0.9+0.99+0.999+"......."" upto 20 terms ")`
`=(7)/(9)[(1-0.1)+(1-0.01)+(1-0.001)+"......."" upto 20 terms "]`
`=(7)/(9)[(1+1+1+"......."" upto 20 terms ")-((1)/(10)+(1)/(10^(2))+(1)/(10^(3))+"......."" upto 20 terms ")]`
`=(7)/(9)[20-((1)/(10)(1-((1)/(10))^(20)))/(1-(1)/(10))]=(7)/(9)[(180-1+10^(-20))/(9)]`
`=(7)/(81)(179+10^(-20))`.
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. A man saves Rs. 200 in each of the first three months of his service. ...

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  3. Let a(n) be the nth term of an AP, if sum(r=1)^(100)a(2r)=alpha " and ...

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  4. If a(1),a(2),a(3),"......" be in harmonic progression with a(1)=5 and ...

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  5. Statement 1 The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+"……."+(...

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  6. If 100 times the 100th term of an AP with non-zero common difference e...

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  7. If x,y,z are in AP and tan^(-1)x,tan^(-1)y,tan^(-1)z are also in AP, ...

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  8. The sum of first 20 terms of the sequence 0.7,0.77,0.777,"……" is

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  9. Let S(n)=sum(k=1)^(4n)(-1)^((k(k+1))/(2))*k^(2), then S(n) can take va...

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  10. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

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  11. If (10)^(9)+2(11)^(1)(10)^(8)+3(11)^(2)(10)^(7)+"........"+(10)(11)^(9...

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  12. Three positive numbers form an increasing GP. If the middle terms in t...

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  13. Let a,b,c be positive integers such that (b)/(a) is an integer. If a,b...

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  14. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

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  15. If m is the AM of two distinct real numbers l and n (l,ngt1) and G(1)...

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  16. Soppose that all the terms of an arithmetic progression (AP) are natur...

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  17. If the 2(nd), 5(th) and 9(th) term of A.P. are in G.P. then find the c...

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  18. If the sum of the first ten terms of the series (1 3/5)^2+(2 2/5)^2+(3...

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  19. Let b(i)gt1" for "i=1,2,"......",101. Suppose log(e)b(1),log(e)b(2),lo...

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  20. For any three positive real numbers a , b and c ,9(25 a^2+b^2)+25(c^2-...

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