Home
Class 12
MATHS
If (10)^9+2(11)^2(10)^7 +….+10 (11)^9 = ...

If `(10)^9+2(11)^2(10)^7 +….+10 (11)^9 = k(10)^9`

A

100

B

110

C

`(121)/(10)`

D

`(441)/(100)`

Text Solution

Verified by Experts

The correct Answer is:
A
The given series can be written as
`k = 1+2(11/10)+3(11/10)^2""+...+9(11/10)^8""+10(11/10)^9" ...(i)"`
On multiplying both sides by `(11/10)`, then
`(11k)/10=(11/10)+2(11/10)^2 +3(11/10)^3""+...+9(11/10)^9""+10(11/10)^10" ...(ii)"`
Now, on subtracting Eq. (ii) frm Eq. (i), then
`-k/10=(11/10)+(11/10)^2""+...+(11/10)^2-10(11/10)^10`
`=(1*{(11/10)^10-1})/((11/10-1))-10(11/10)^10`
`rArr" "k = -100*{(11/10)^10-1}+100(11/10)^10 = 100`
Promotional Banner

Similar Questions

Explore conceptually related problems

If (10)^(9)+2(11)^(1)+(10)^(8)+3(11)^(2)(10)^(7)+…+10(11)^(9)=k(10)^(9) then k is equal to

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

The value of ""^(10) C_(2) + ""^(10) C_(3) + … + ""^(10) C_(9) is

int (10x^(9)+10^(x) log (10))/(10^(x)+x^(10)) dx

State with reason whether following functions have inverse (i) f : {1,2,3,4} to {10} with f = {(1,10), (2,10), (3,10) ,(4,10)} (ii) g: {5,6,7,8} to {1,2,3,4} with g = {(5,4) , (6,3), (7,4), (8,2)} (iii) h : {2,3,4,5} to {7,9,11,13} with h = {(2,7), (3,9) , (4, 11), (5,13)}

The sum (1)/(2)""^(10)C_(0)-""^(10)C_(1)+2.""^(10)C_(2)-2^(2)*""^(10)C_(3)+ . . .+2^(9)*""^(10)C_(10) equals:

The value of sum_(k=1) ^(10)( sin "" ( 2kpi )/( 11) + i cos "" ( 2kpi )/(11)) is :

If (4)^(log_(9) 3)+(9)^(log_(2) 4)=(10)^(log_(x) 83) , then x is equal to

A proton beam enters a magnetic field of 10^(-4) " Wb " m^(-2) Wb normally. If the specific charge of the proton is 10^(11) " C " kg^(-1) and its velocity is 10^(9) " m "s^(-1) then the radius of the circle described will be