FEDERAL BOARD
Composed by Engin Baştürk
TYPE
Subjective
Sequences and Series
XI
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CLASS
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No
8
1 1
3 9
Q1:
Find the sum of first 15 terms of the geometric sequence 1, , ,...
Q2:
Sum to n terms, the series .2  .22  .222  ...............
Q3:
Sum to n terms, the series 3  33  333  ...............
Q4:
Sum to n terms, the series 1   a  b   a 2  ab  b2  a3  a 2b  ab2  b3  ...
Q5:
Sum to n terms, the series r  1  k  r 2  1  k  k 2 r 3  ........
Q6:
1
Sum the series 2  1  i      .... to 8 terms.
i
Q7:
Find the sums of the infinite geometric series

 



1 1
1
 
 ......
5 25 125
1 1 1
Find the sums of the infinite geometric series    ......
2 4 8
Q8:
9 3
2
  1   ..........
4 2
3
Q9:
Find the sums of the infinite geometric series
Q10:
Find the sums of the infinite geometric series 2  1  0.5  ........
Q11:
Find the sums of the infinite geometric series 4  2 2  2  2  1  ........
Q12:
Find the sums of the infinite geometric series 0.1  0.05  0.025  .......
Q13:
Find vulgar fraction equivalent to the 1.34 recurring decimal.
Q14:
Find vulgar fraction equivalent to the 0.7 recurring decimal.
Q15:
Find vulgar fraction equivalent to the 0.259 recurring decimal.
Q16:
Find vulgar fraction equivalent to the 1.53 recurring decimal.
Q17:
Find vulgar fraction equivalent to the 0.159 recurring decimal.
Q18:
Find vulgar fraction equivalent to the 1.147 recurring decimal.
Q19:
Find the sum to infinity of the series; r  1  k  r 2  1  k  k 2 r 3  ........ r and k being proper fractions
PAKTURK


Success is a ladder you cannot climb with your hands in your pockets
1
Q20:
If y 
2y
x 1 2 1 3
 x  x  ... and 0  x  2 , then show that x 
1 y
2 4
8
Q21:
If y 
3y
3
2
4
8 3
x  x2 
x  ... and 0  x  , then show that x 
2 1  y 
2
3
9
27
Q22:
A ball is dropped from a height of 27 meters and it rebounds two-third of the distance it falls. If it continues to fall in the
same way what distance will it travel before coming to rest?
Q23:
What distance will a ball travel before coming to rest if it is dropped from a height of 75 meters and after each fall it
rebounds
2
of the distance it fell?
5
y 1
and find the interval in which the series is convergent.
2y
Q24:
If y  1  2 x  4 x 2  8x3  ... , then show that x 
Q25:
If y  1 
Q26:
The sum of an infinite geometric series is 9 and the sum of the squares of its terms is
PAKTURK
 y 1 
x x2
  ........... , then show that x  2 
 and find the interval in which the series is convergent.
2 4
 y 
81
. Find the series.
5
Success is a ladder you cannot climb with your hands in your pockets
2