Solve: `(3n + 8)/ (7n -4) = 1 `

Solve : (2)/(3)(n+6) - (1)/(5)(n-4) = (3)/(7)(n+12)

Sahil tried to solve an equation but couldn't reach to the correct answer. Following were the steps performed by him to solve the expression. Solve for n: 3n + 5(n + 2) = 46 Step 1 : 3n+ 5n + 10 = 46 Step 2: 8n + 10 = 46 Step 3: 8n = 56 Step 4: n= 56/8 = 7 Find the incorrect step.

(1) / (3.7) + (1) / (7.11) + (1) / (11.15) + ...... + (1) / ((4n-1) (4n + 3)) = (n ) / (3 (4n + 3))

Solve :(a)3n+7=25 (b) 2p-1=23

If n is any positive integer , show that 2^(3n +3) -7n - 8 is divisible by 49 .

Using binomial theorem, prove that (2^(3n)-7n-1) is divisible by 49, where n in N.

Using the principle of mathematical induction, prove each of the following for all n in N 1/(1*4)+1/(4*7) + 1/(7*10) +…+1/((3n-2)(3n+1)) = n/((3n+1)) .