Question

A = 1/2x3 + 1/3x4 + /4x5+...+ 1/50x51
B = 4/1x5 + 4/5x9 + 4/9x13 +...+ 4/97x101

Answer 1

`A=1/(2xx3) + 1/(3xx4) + 1/(4xx5) + ... + 1/(50xx51)`

`= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 -1/5 + ... + 1/50 - 1/51`

`= 1/2 - 1/51`

`= 49/102`

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`B= 4/(1xx5) + 4/(5xx9) + 4/(9xx13) + ... + 4/(97xx101)`

`= 1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/97 - 1/101`

`= 1- 1/101`

`= 100/101`

Answer 2

a: =1/2-1/3+1/3-1/4+...+1/50-1/51

=1/2-1/51=49/102

b: =1-1/5+1/5-1/9+1/9-1/13+...+1/97-1/101

=1-1/101=100/101