wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

The value of limn{(n3+1)(n3+23)(n3+33)........(n3+n3)n3}1n is equal to α.eβx31+x3dx, where αϵN,βϵR,then find αβ.___


Open in App
Solution

y=limn{(n3+1)(n3+23)(n3+33)........(n3+n3)n3}1n
Taking log on both sides, we get
logy=limn1n{nr=1log(n3+r3)logn3}logy=limn1nnr=1log[1+(rn)3]logy=10log(1+x3)dxlogy=[log(1+x3).x]10103x21+x3xdxlogy=log2310x21+x3xdx y=2.e310x31+x3αβ=2(3)=5


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Nth Derivative Test
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon