How do you estimate values via Binomial Expansion??

For example...
Expand (1 + 2x)^6 in ascending powers of x up to the term in x^3... Fair enough...

THEN IT SAYS: Using your expansion, approximate the value of (1.02)^6... How the hell do you do that! And obviously you have show your working! I cant find how 2 do this anywhere! HELP!!

Reply 1

rbnphlp

11

Greeze Geez

For example...
Expand (1 + 2x)^6 in ascending powers of x up to the term in x^3... Fair enough...

THEN IT SAYS: Using your expansion, approximate the value of (1.02)^6... How the hell do you do that! And obviously you have show your working! I cant find how 2 do this anywhere! HELP!!

comparing the two expressions let 1+2x=1.02 ,find the value of x..
and simply sub that into your expansion

Reply 2

Greeze Geez

OP

6

Safe! So weve got: 1 + 12x + 60x^2 + 160x^3

1+2x=1.02 => x=0.01

1+12(0.01)+60(0.01)^2+160(0.01)^3= 1.1262 (4 d.p)

Yea Boiiiii! Thanx for the help mate!

no worries

Original post by Greeze Geez

For example...
Expand (1 + 2x)^6 in ascending powers of x up to the term in x^3... Fair enough...

THEN IT SAYS: Using your expansion, approximate the value of (1.02)^6... How the hell do you do that! And obviously you have show your working! I cant find how 2 do this anywhere! HELP!!