1)

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


A) 781(1791020)

B) 79(991020)

C) 781(179+1020)

D) 79(99+1020)

Answer:

Option C

Explanation:

 Let S=0.7+0.77+0.777+.....=  710+77102+777103+....  + up to 20 terms

=7[110+11102+111103+....upto20terms]

   =79[910+99102+999103+....upto20terms]

  =79[(1110)+(11102)+(11103)+....upto20terms]

=79[(1+1+......+upto20terms)(110+1102+1103+....upto20terms)]

=79[20110{1(110)20}1110]

[    20i=1=20  and sum of n terms of GPS   sn=a(1rn)1r when (r<1)]

   =79[2019{1(110)20}]

 =79[1799+19(110)20]

 =781[179+(10)20]