IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

srichaitanya

₁₀₀

_N

_[_]

(N+R)¹⁰/N¹⁰+10¹⁰

^R=1

nitin62225

ans=100

soln:

_{[ r=1]}

^{[ 100]} 1=100

iitkgp_bipin

_[N]

_[infinity] (N+R)¹⁰/(N¹⁰ + R¹⁰)

Divide numerator and denominator by N¹⁰.

_[N]

_[infinity] (1 + R/N)¹⁰/ (1 + R¹⁰/N¹⁰) = 1

Hence the summation would become :

S = _[R=1]

^[100] 1 = (1+1+1............100 times) = 100

Hence the result is 100.

elessar_iitkgp

Ultimate solution Bipin. Excellent work