Question

The unit digit of 1' +11"+11111+........1111111111111111 is​

Answer 1

Answer:

Consider the following composite series,

1+11+111+1111+…+(1111…n 1's)

=1+(1+10)+(1+10+100)+(1+10+100+1000)+…+(1+10+100+1000+…+10n−1G.P with n number of terms)

Each term of above series is sum of a G.P. whose first term is 1 & common ratio is 10 hence nth term of above series is Tn=1⋅(10n−1)10−1=10n−19

Hence, the sum (Sn) of n terms of such series having nth term Tn=10n−19 is given as

Sn=∑n1Tn=∑n110n−19=19∑n1(10n−1)=19(∑n110n−∑n11)

=19(10(10n−1)10−1−n)=181(10(10n−1)−9n)

Hence, the generalized formula to get sum of n terms of this composite series

[Math Processing Error]

hence substituting n=5 in the above generalized formula for given series 1+11+111+1111+11111 having five terms, the sum is given as

1+11+111+1111+11111=181(10(105−1)−9⋅5)=12345

Alternatively, one can fairly easily add all five terms of given series as follows

1+11+111+1111+11111––––––––=12345

Step-by-step explanation:

pl mark brainliest

hope this helps

good night