(a) \(\frac{10}{9}\) (10100 – 1) – 100
Let S100 = 9 + 99 + 999 + ...... upto 100 terms
= (10 – 1) + (100 – 1) + (1000 – 1) + ..... + upto 100 terms
= (10 + 102 + 103 + .... upto 100 terms) – (1 + 1 + 1 + ..... upto 100 terms)
= \(\frac{10(10^{100}-1)}{10-1}-100\) \(\bigg(\because\,S_n=\frac{a(r^n-1)}{r-1}\,\text{when}\,r>1\bigg)\)
= \(\frac{10}{9}\) (10100 – 1) – 100.