If n is a natural number , then n(n +1) (n +2) (n +3) +1 is always:
If n is a natural number , then n(n +1) (n +2) (n +3) +1 is always:
यदि n एक प्राकृतिक संख्या है, तो n(n +1) (n +2) (n +3) +1 हमेशा होगा:
Detailed Solution & Logic
Correct Answer:
A perfect square / एक पूर्ण वर्ग
The expression $n(n+1)(n+2)(n+3)+1$ can be rewritten as
$ n(n+3)(n+1)(n+2)+1 = (n^2+3n)(n^2+3n+2)+1 $.
Let $x = n^2 + 3n$.
Then the expression becomes
$ x(x+2)+1 = x^2 + 2x + 1 = (x+1)^2 $.
So, $n(n+1)(n+2)(n+3)+1$ is always a perfect square.
Similar Practice Questions
Ram, Ravi and Reena can complete a piece of work in 16, 20 and 24 days respectively. They started the work together but Ravi left 5 days before the completion of the work. In how many days did the other two together complete the work?
Ram, Ravi and Reena can complete a piece of work in 16, 20 and 24...
2 times the present age of X is 7 years less than 6 times the present age of Y.
2 times the present age of X is 7 years less than 6 times the...
If A : B = 3 : 7 and B : C = 2 : 5, then find the value of A : B : C.
If A : B = 3 : 7 and B : C = 2 :...
A circular jogging track has a radius of 50 m. A runner covers a curved path that subtends an angle of $120^\circ$ at the center. What is the length of the arc she runs?
A circular jogging track has a radius of 50 m. A runner covers a curved...
Two types of tea are mixed. The first type costs ₹18 per kg and the second type costs ₹20 per kg. In what ratio should these be mixed so that by selling the mixture at ₹21 per kg, a profit of 10% is gained?
Two types of tea are mixed. The first type costs ₹18 per kg and the...
The average of the number 253, 245, 325, 120 and 115+2k is 212
The average of the number 253, 245, 325, 120 and 115+2k is 212. Find the...
The price of milk has increased by 20%. To keep the expenditure unchanged, current consumption must be reduced by:
The price of milk has increased by 20%. To keep the expenditure unchanged, current consumption...