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

If `(10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7+...........+10 (11)^9= k (10)^9` , then k is equal to :

A

`121/10`

B

`441/100`

C

100

D

110

Text Solution

Verified by Experts

The correct Answer is:
C
`S=10^(9)+2cdot11^(1)cdot10^(8)+…+10cdot11^(9)`
`therefore11/10cdotS=11^(1)cdot10^(8)+..+9cdot11^(9)+11^(10)`
Subtracting
`rArr-1/10cdotS=10^(9)+11^(1)cdot10^(8)+11^(2)cdot10^(7)+…+11^(9)-11^(10)`
`rArr-1/10S=10^(9)(((11/10)^(10)-1)/(11/10-1))-11^(10)`
`rArr-1/10S=11^(10)-10^(10)-11^(10)`
`rArrS=10^(11)`
`rArrS=100cdot10^(9)`
`rArrk=100`
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