What value is S? S=(π^2/2!)-(π^4/4!)+(π^6/6!) -/+....

Question

What value is S?

S=(π²/2!)-(π⁴/4!)+(π⁶/6!) -/+....

Answer 1

cosx = 1 - x²/2! + x⁴/4! + x⁶/6! + ...

Let x = π, then cosπ = 1 - (π²/2!) + (π⁴/4!) - (π⁶/6!) + ....

From here S = (π²/2!) - (π⁴/4!) + (π⁶/6!) - ... = 1 - cosπ = 2 ...