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The product of four consecutive natural numbers plus one is

A) anon-square
B) always sum of two square numbers
C) a square
D) None of these

Correct Answer:



C) a square

Description for Correct answer:
Let the four consecutive natural number be x, x+1, x+2, x+3

Now product of four consecutive natural number plus one

=x(x + 1)(x + 2)(x + 3) + 1 ... (i)

i.e.

for

\( \Large x = 1 (1 X 2 X 3 X 4) + 1 = 25 =(5)^{2}\)

for x = 2

\( \Large ( 2 x 3 x 4 x 5) + 1 = 121 = (11)^{2} \)

for x = 3

\( \Large (3 x 4 x 5 x 6) + 1 = 361 = (19)^{2} \)

for x = 4

\( \Large (4 x 5 x 6 x 7) + 1 = 841 = (29)^{2} \)

Hence for any value of x, equation square number.

option (c) is correct.

Part of solved CDS Maths(2) questions and answers : Exams >> CDSE >> CDS Maths(2)

Comments

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