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Question Number 159999 by Tawa11 last updated on 23/Nov/21

Answered by Kunal12588 last updated on 23/Nov/21

$$(1-x^n)=(1-x)(1+x+x^2+x^3+x^4+...+x^{n-1})$$$$\int \frac{1-x^{100}}{1-x}dx=\int (1+x+x^2+x^4+...+x^{99})dx$$$$=x+\frac{1}{2}{x}^2+\frac{1}{3}{x}^3+...+\frac{1}{100}{x}^{100}=\underset{k=1}{\sum ^{100}}\frac{x^k}{k}$$

Commented by Tawa11 last updated on 24/Nov/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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