IIT JEE , AIEEE Forum - Mathematics , Algebra

vivek_aero

How to find the summation of 1/n(n+1)

sboosy

(k=1 to n) [ 1/k(k+1) ]

=>

[1/k - 1/(k+1) ]

=>

1/k -

1/(k+1)

=> 1+1/2+1/3+...1/n - 1/2-1/3-....1/(n+1)

=> 1-1/(n+1)

=> n/(n+1)

vivek_aero

Re:How to find the summation of 1/n(n+1) thanks,don't know why this didn't occur to me

ganesha1991

_{sorry guys tanx for the correction}

anandghegde

How did you write 1/n(n+1) = 1+1/n????????

The first step itself is wrong

anandghegde

even if it was correct, how did you get
_{1 ]}

^{[m ]} 1/n = 1/ [ m(m+1)/2]??????
Did you write this on this basis???
_{[ ]}

^{[ ]} n = n(n+1)/2

anandghegde

How did you get = m + 2/ m(m+1)
= [m² (m+1) + 2 ] / 2??????

A whole lot of mistakes man!!

akhil_o

edited....sorry
ans is n/n+1 as sboosy said

aks_0123456

t_n⁼ 1/k - 1/(k+1)
= [1-1/2]+[1/2-1/3]+.......................[1/k-1/k+1]
=1-(1/k+1)

this is the shortest way...............

ganesha1991

tanx for the correction.............i'm not gud in algebra.................tanx guys

prash_shan_jpr

Hey d ans is-

n/n+1

ganesha1991

bro....i did the same mistake.........check out the mistake corrected by anand ............and u didn't do summation at all

vineetnegi

A=1/n(n+1)

A=1/n-1/(n+1)

sum(a)=1-1/(n+1)..................through telescoping technique