Question

S=2/1.2+2/2.3+2/3.4+............+2/98.99+2/99.100

Answer 1

mk k vt lại đề nha

S=2.(1/1.2+1/2.3+1/3.4+............+1/99.100)

S=2.(1-1/2+1/3-1/4+1/4-1/5+.............+1/99-1/100)

S=2.(1-1/100)

S=2.99/100

S=198/100

Answer 2

S=\(\frac{2}{1.2}\)+\(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)+...+\(\frac{2}{98.99}\)+\(\frac{2}{99.100}\)

S=\(\frac{2}{1}\).(\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+...+\(\frac{1}{98.99}\)+\(\frac{1}{99.100}\))

S=\(\frac{2}{1}\).(\(\frac{1}{1}\)-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+...+\(\frac{1}{98}\)-\(\frac{1}{99}\)+\(\frac{1}{99}\)-\(\frac{1}{100}\))

S=\(\frac{2}{1}\).(\(\frac{1}{1}\)-\(\frac{1}{100}\))

S=\(\frac{2}{1}\).(\(\frac{100}{100}\)-\(\frac{1}{100}\))

S=\(\frac{2}{1}\).\(\frac{99}{100}\)

S=\(\frac{99}{50}\)

Vậy S=\(\frac{99}{50}\)