The value of e^ ₁₀ 1^ + ₁₀ 2^ + ₁₀ 3^ + + ₁₀ 89^ is

Step-by-step solution

We know that aligned & (90^ - )= =1 & 1^ 89^ = 2^ 88^ = 3^ 87^ aligned = 44^ 46^ =1 So, ₁₀ 1^ + ₁₀ 2^ ₁₀ 89^ aligned = ( ₁₀ 1^ + ₁₀ 89^ ) & + ( ₁₀ 2^ . & .+ ₁₀ 88^ ) + + ( ₁₀ 44^ . & .+ ₁₀ 46^ ) & + ₁₀ 45^ aligned array r = ₁₀ ( 1^ + 89^ )+ ₁₀ ( 2^ + 88^ ) + + ₁₀ ( 44^ + 46^ ) + ₁₀ 45^ = ₁₀ 1+ + ₁₀ I+ ₁₀ 1 array =0 Thus, e^ .e ₁₀ 1^ + ₁₀ 2^ + + ₁₀ 89^ ) [ ₁₀ 1=0 ]=e^0=1