Question

B=1+1/3+1/6+1/10+....+1/630 = ?

Answer 1

B = \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{630}\)

B = \(1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{1260}\)

B = \(1+2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{35.36}\right)\)

B = \(1+2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..+\frac{1}{35}-\frac{1}{36}\right)\)

B = \(1+2.\left(\frac{1}{2}-\frac{1}{36}\right)=1+2.\frac{17}{36}=1+\frac{17}{18}\)

B = \(\frac{35}{18}\)

Answer 2

(x+1) + (x+4) + (x+7) + ....+ (x+28) = 155