Problem: The limiting sum of the infinite series, 101+1022+1033+… whose nth term is 10nn is:
Answer Choices:
A. 91
B. 8110
C. 81
D. 7217
E. larger than any finite quantity
Solution:
Write the given series as:
101+1021+1031+1041++1021+1031+1041++1031+1041+……… and so forth
Let s1 be the limiting sum of the first-row series, s2, that of the second-row series, and so forth.
s1s2s3=1−101101=91,=1−1011021=901,=1−1011031=9001,and so forth.
and so forth.
Therefore, the required limiting sum equals
91+901+9001+…=1−10191=8110