SOLUTION: Find the sum of the first 100 terms in the series 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n*(n+1))

SOLUTION: Find the sum of the first 100 terms in the series 1/(12) + 1/(23) + 1/(34) + ... + 1/(n(n+1))

Algebra.Com

Question 1089864: Find the sum of the first 100 terms in the series
1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n*(n+1))
Answer by ikleyn(52855) (Show Source): You can put this solution on YOUR website!
.

    =     ( represent each term  as the difference . You will get )


=  ()) + () + (}} + . . . + () =    ( cancel all intermediate terms ) = 


=  .

Answer. .

RELATED QUESTIONS
find the sum of following series:... (answered by Edwin McCravy)

(1/1*2)+(1/2*3)+(1/3*4)+.........find the sum of n terms of the given... (answered by Fombitz)

Find the sum of series {{{ 1 + (1^n/2)C1 + (1^n/3)C2 + (1^n/4)C3 + ...... (answered by ikleyn)

If there are (2n+1) terms in an arithmetic series, prove that the ratio of the sum of odd (answered by richard1234)

Find the sum of n terms of series... (answered by Edwin McCravy)

Find the sum of the series {{{ 1 + (1^n/2)C_1 + (1^n/3)C_2 + (1^n/4)C_3 + upto... (answered by ikleyn)

1(1!) + 2(2!) + 3(3!) + . . . + n(n!). Find the sum of this series if n =... (answered by richard1234)

Find the sum of the first n terms of the following series 1-4+9-16+---- (answered by solver91311)

sum of the first 100 terms for the series:... (answered by kensson,palanisamy)