एक धन पूर्णांक n के लिए, माना
` a(n) = 1 + 1/2 + 1/3 + 1/4 + ……. + (1)/(2^n - 1) ` तब

For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/ ((2^n)-1) Then

L 1 n → ∞ 1 + 1 2 + 1 4 + ... ... + 1 2 n 1 + 1 3 + 1 9 + ... . . + 1 3 n

By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , n in N

Monosomics are: 1. n 2. 2n +1 3. 2n - 2 4. 2n - 1

For a positive integer n, let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+ . . .+(1)/(2^(n)-1) Then:

For a positive integer n let a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1) then

lim_ (n rarr oo) (1) / (n) [(1) / (n + 1) + (2) / (n + 2) + ... + (3n) / (4n)]

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

lim_ (n rarr oo) (((n ^ (5) +2) ^ ((1) / (4))) - ((n ^ (2) +1) ^ ((1) / (3))) ) / ((n ^ (4) +2) ^ ((1) / (5)) - (n ^ (3) +1) ^ ((1) / (2))) is