question for GP
find the sum of first n terms of:
1) 4 + 44 + 444 +.............
2) 0.7 + 0.77 + 0.777 +.............
Answers
Answered by
1
here is your answer...
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tarush93:
it has formulae b^2=ac
oh I am so sorry
yep
u can see second answer its gp
I don't know this answer
yes second answer is right?
yess it is
okay but i dont know 1
sorry
can you take my answer as brainlist one
Answered by
3
1 ). 4 + 44 + 444 +....
4 / 9 [ 9 + 99 + 999 .... n ]
=> 4/9 [ (10 - 1) + ( 10^2 - 1 ) + ( 10^3 - 1 )....( 10^(n) - 1]
=> 4 / 9 [ ( 10 + 10^2 + 10 ^3..) - n]
=> 4 / 9 [ 10 { 10^( n ) - 1 } / ( 10 - 1 ) - n ]
=> 4 / 81 [ 10 { 10^( n ) - 1 } - n ]
2 ). 0.7 + 0.77 +0.777.......
7/ 10 + 7/ 100 + 7 / 1000....
=>7 [ 1 / 10 + 1 / 100 + 1 / 1000....]
=> 7 [ 1/ 10 { 1 - 1 / 10^n } / { 1 - (1 / 10) }
=> 7 [ 1 / 10 { 1 - 1 / 10^n } / 9 / 10 ]
=> 7 [ 1 - ( 1 / 10^n ) / 9 ]
4 / 9 [ 9 + 99 + 999 .... n ]
=> 4/9 [ (10 - 1) + ( 10^2 - 1 ) + ( 10^3 - 1 )....( 10^(n) - 1]
=> 4 / 9 [ ( 10 + 10^2 + 10 ^3..) - n]
=> 4 / 9 [ 10 { 10^( n ) - 1 } / ( 10 - 1 ) - n ]
=> 4 / 81 [ 10 { 10^( n ) - 1 } - n ]
2 ). 0.7 + 0.77 +0.777.......
7/ 10 + 7/ 100 + 7 / 1000....
=>7 [ 1 / 10 + 1 / 100 + 1 / 1000....]
=> 7 [ 1/ 10 { 1 - 1 / 10^n } / { 1 - (1 / 10) }
=> 7 [ 1 / 10 { 1 - 1 / 10^n } / 9 / 10 ]
=> 7 [ 1 - ( 1 / 10^n ) / 9 ]
Thanks. :-)
tyy
Thnx
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