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Q 1 ) limx---->∞ (√ x √ x + √x - √ x )
Q 2) limx---->∞ x3/2 √ x3 + 1 - √ x3 - 1
ans : 1
Q 3) limx---->∞ 1/ 1-n4 + 8 / 1-n4 + ........... + n3 / 1-n4
ans: - 1 / 4
?
the answer is infinity
Ans 3.
(1+ 8 + 27 + ... + n3)/1-n4
Since 13+23+33+...+n3 = (n(n+1))2/4 then
the expression becomes (n(n+1))2/4(1-n4)
= ((n)2(n+1)2)/4(1-n4)
dividing the whole expression ny n4 . Now the expression is
=(1)(1+1/n2))/4(1/n4-1)
= No since n->infinity 1/n tends to 0 thus byu using direct substitutions
= 1/-4 =-1/4
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