`1+1/(1+2)+1/(1+2+3)+1/(1+2+3+n)=(2n)/(n+1)`

Using the principle of mathematical induction prove that 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1) for all n in N

Using the principle of mathematical induction prove that 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)++1/(1+2+3++n)=(2n)/(n+1) for all n in N

Using the principle of mathematical induction prove that 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+... +1/(1+2+3+..+n) =(2n)/(n+1) for all n in N

Using the principle of mathematical induction prove that 1+(1)/(1+2)+(1)/(1+2+3)+(1)/(1+2+3+4)+...+(1)/(1+2+3+...+n)=(2n)/(n+1) for all n in N

lim_ (n rarr oo) [(1+ (1) / (n ^ (2)))) (1+ (2 ^ (2)) / (n ^ (2))) (1+ (3 ^ (2) ) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2)))] ^ ((1) / (n))

lim_ (n rarr oo) (1+ (1) / (2) + (1) / (2 ^ (2)) + (1) / (2 ^ (3)) + ...... (1) / (2 ^ (n))) / (1+ (1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) ...... (1) / (3 ^ (n)))

For all ngt=1 , prove that , (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + ……+ (1)/(n(n+1)) = (n)/(n+1)

1/1.2 + 1/2.3 +…..+ 1/(n(n+1)) = n/(n+1)

(1)/(n)+(1)/(n+1)+(1)/(n+2)++(1)/(2n-1)=1-(1)/(2)+( 1)/(3)-(1)/(4)++(1)/(2n-1)

Prove by the principle of mathematical induction that for all n belongs to N :\ 1/(1. 3)+1/(3.5)+1/(5.7)++1/((2n-1)(2n+1))=n/(2n+1)