What is 1 ₂ ~N + 1 ₃ ~N + 1 ₄ ~N + .+ 1 ₁₀₀ ~N equal to ( N 1) ?

Step-by-step solution

aligned & 1 ₂ ~N + 1 ₃ ~N + 1 ₄ ~N + + 1 ₁₀₀ ~N & = 1 ~N 2 + 1 ~N + 1 3 + + 1 ~N 4 & ( _ a b = b N ) & = 2 ~N + 3 ~N + 4 ~N + .+ 100 ~N & = 2+ 3+ 4+ .+ 100 ~N & = (2.3 .4 .100) N aligned = 100! N = 1 ~N 100! = 1 _ 100! N