IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

srichaitanya

_{[n ]}

_{[infinity ]} a^n_bⁿ/aⁿ+bⁿ

rphy

is it given that a or b is less than 1??

elessar_iitkgp

If a & b are both +ve or both -ve
If a>b
b/a < 1
So transform as
_n

(1-(b/a)ⁿ)/(1+(b/a)ⁿ) = 1
For a fraction raised to a large power tends to zero.
If a=b, the limit is 0
If a<b
a/b < 1
Transform as
_n

((a/b)ⁿ -1)/((a/b)ⁿ+1) = -1

If a>0, b<0
If a>|b|
|b|/a < 1
So transform as
_n

(1-(b/a)ⁿ)/(1+(b/a)ⁿ) = 1
If a<|b|
a/|b| < 1
Transform as
_n

((a/b)ⁿ -1)/((a/b)ⁿ+1) = -1

If a<0, b>0
If |a|>b
b/|a| < 1
So transform as
_n

(1-(b/a)ⁿ)/(1+(b/a)ⁿ) = 1
If a<|b|
a/|b| < 1
Transform as
_n

((a/b)ⁿ -1)/((a/b)ⁿ+1) = -1

amar.gupta

good work elessar_iitkgp

elessar_iitkgp

Thanx