Question

Using mathematical induction, prove that 1.2.3 + 2.3.4 + 3.4.5 + ... Upto n terms = $\frac{n(n + 1)(n + 2)(n + 3)}{4}$ for all n ∈ N

Answer 1

hope it helps u..............................

Answer 2

Solution :

1.2.3+2.3.4+...up to n terms

= [n(n+1)(n+2)(n+3)/4]

Let S(n) be the given statement

For n = 1

LHS = 1.2.3 = 6

RHS = [ 1(2)(3)(4)]/4 = 6

Assume S(k) is true .

1.2.3+2.3.4+ ..+k(k+1)(k+2)

= [ k(k+1)(k+2)(k+3)/4 ]

Adding (k+1)(k+2)(k+3) on both sides

Therefore ,

1.2.3+2.3.4+..+k(k+1)(k+2)+(k+1)(k+2)(k+3)

= [k(k+1)(k+2)(k+3)/4 ]

S(k+1) is true.

Hence , S(n) is true for all n€N

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