Question

1\2 + 1\6 + 1\12 ... + 1\9900 + 1\10100 = ?

Answer 1

    1/2 + 1/6 + 1/12 + ... + 1/9900 + 1/10100

= 1/1.2 + 1/2.3 + 1/3.4 +... +1/99.100 + 1/100.101

= 1/1 - 1/2 + 1/2 + 1/3 - 1/3 + 1/4 +... + 1/99 - 1 / 100 + 1/100 - 1/101

= 1/1 - 1/101

= 100 /101

Answer 2

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{9900}+\frac{1}{10100}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{99.100}+\frac{1}{100.101}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}\)

=\(1-\frac{1}{101}\)

=\(\frac{100}{101}\)

Answer 3

= 1/1x2 + 1/2x3 + 1/3x4 + .... + 1/99x100 + 1/100x101. = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/99 - 1/100 + 1/100 - 1/101 = 1 - 1/101 = 100/101

Answer 4

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Answer 5

`1/2 + 1/6 + 1/12 + ... + 1/10100`

`= 1/(1 . 2) + 1/(2 . 3) + 1/(3 . 4) + ... + 1/(100 . 101)`

`= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/100 + 1/100 - 1/101`

`= 1/1 - 1/101`

`= 100/101`