Question

Compute the first four partial sums S1, 2=1 as follows. 3 SĄ for the series having nth term An starting with an = (-1)"+15 S1 = S2 = S3 = S4=

Answer 1

I am attaching the pictures of solution. If you find my answer helpful please press thumbs up button. Thanks

inti Ans given an= (-1) 5 Now put n=1 in 0 - a = tolt's و (1) 5 3 0,= 5- Putting n=2 in 0 :- a = (-+ 5 =(-135 =) a = -52 na3 in 0:- Az =(-1) 5 = (-1) 5 - a₂ = 5 5-6 putting 3+)

putting n=4 in 0:- au = [gtig =(-155 ay=-5 - =) Now si = a, =) S, = 5 (by @) similarly S2 = a, ta - 5 - 5 (by 083) --- And Sz= a, tat az = 5-5+5 (by @319) = S₂ = 5

And Sy=9, +2 +93 tay - 5-5+5-5 (by ,, & Sy = =0 so answers are S, = 5 Se= Sz= Sy=To

Ans given sum is 2 - 2+2-8 (-1°&+ ED'& +61) 2+ 602+--- E (-) 2 n-o so answer is 8 Win mzo