Altering sign sequence

Find the nth term of the sequence -1/2, 1/4, - 1/6, 1/8, - 1/10, ....

Final Answer:

a_n = (-1)^n/(2n)

Step-by-step explanation:

a1​=−1/2=−21​=−0.5 a2​=1/4=41​=0.25 a3​=−1/6=−61​≐−0.1667 a4​=1/8=81​=0.125 a5​=−1/10=−101​=−0.1  sgn −+−+−  an​=2n(−1)n​   Verifying Solution:  A1​=2⋅ 1(−1)1​=−21​=−0.5 A2​=2⋅ 2(−1)2​=41​=0.25 A3​=2⋅ 3(−1)3​=−61​≐−0.1667 A4​=2⋅ 4(−1)4​=81​=0.125 A5​=2⋅ 5(−1)5​=−101​=−0.1 A6​=2⋅ 6(−1)6​=121​≐0.0833 A7​=2⋅ 7(−1)7​=−141​≐−0.0714  an​=(−1)n/(2n)

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