Sequence and series

[hexed plume]

My answer is -3ln2 + 7/4, koi confirm krna solve krke

[last shore]

<@&1227988399579730072>

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[empty cliff]

tell me which step you got confused

@hexed plume

approach is basic break that term into 2 pieces 1st

[hexed plume]

i didnt get confused but idk if my answer is correct or not

i used partial fractiond decomp initially

and got 1/2^r ( -r + 3 -2/3 + 1/r+1)

[empty cliff]

11th me itna padh lia ??

good

[hexed plume]

then used that summation r = 1 to inf r/2^r = 2

and kyuki 2 se start hai toh minus 1/2 kr diya

[empty cliff]

idk answer

your approach is fine

[hexed plume]

and 3.summation r = 2 to inf ( 1/2^r) = 3/2 aagya

toh first 2 kat gye

ab bache jo hai voh crazy hain

[empty cliff]

i got your point

[hexed plume]

kyuki summation r = 2 to inf (-2/2^r.r)

uske liye i used

[empty cliff]

basic miscellaneous series

[hexed plume]

summation r = 1 to inf (x^2/r) = -ln(1-x)

[empty cliff]

your approach is correct

[hexed plume]

so first one me r = 1/2 daal diya direct

second mie needed to divide by r and substitute r = k+1

[empty cliff]

ok

[hexed plume]

hn early starter benefits ig

toh sahi hai method?

like last 2 ka poochna hai mainly

[empty cliff]

partial fraction laga lia

[hexed plume]

summation x^2/r r = 1 to inf = -ln(1-x) vala

[empty cliff]

to your ans will come faster

[hexed plume]

vahi kra hia

[empty cliff]

and ofc other things is correct

good bruv

2027 wont go soo bad

[hexed plume]

lol

hope se

kohinoor ahh

[empty cliff]

nah bro kafi log bade ajeeb hai

tumhare jaise log will score early starters