WHAT IS D VALUE OF 1*2*3*4+2*3*4*5+3*4*5*6+..........N

shael shekhawat

akshat aggarwal

is the nth term is n^4+6n^3+11n^2+6nplzzzz reply then only i will proceed this question

Akshay

T_r = r(r+1)(r+2)(r+3)

Consider a sequence V_r such that,

V_r = r(r+1)(r+2)(r+3)(r+4)

Therefore, V_r-1= (r-1)r(r+1)(r+2)(r+3)

V_r - V_r-1 = r(r+1)(r+2)(r+3)(-r+1 r+4)

= r(r+1)(r+2)(r+3)(5)

I.e. V_r - V_r-1 = 5T_r

So V₁-V₀ = 5T₁

V₂-V₁ = 5T₂

V₃-V₂ = 5T₃ and so on till, V_N - V_N-1 = 5T_N

Adding all these equations gives, T₁+T₂+.....+T_N = (V_N-V₀)/5

Thus Sum = {N(N+1)(N+2)(N+3)(N+4)}0.2