lim n → ∞ n n 2 + 1 2 + n n 2 + 2 2 + n n 2 + 3 2 + . .   … . + 1 5 n 2 is equal to

Question

lim n &#8594; &#8734; n n 2 + 1 2 + n n 2 + 2 2 + n n 2 + 3 2 + . . &#160; &#8230; . + 1 5 n 2 is equal to

Aicharya · Accepted Answer

To find, lim n &#8594; &#8734; n n 2 + 1 2 + n n 2 + 2 2 + &#8230; + n n 2 + 2 n 2 = &#8721; r = 1 2 n n n 2 + r 2 = 1 n &#8721; r = 1 2 n 1 1 + r n 2 &#160; &#160; = &#8747; 0 2 1 1 + x 2 d x = tan - 1 &#8289; x 0 2 = tan - 1 &#8289; 2 .

lim n &#8594; &#8734; n n 2 + 1 2 + n n 2 + 2 2 + n n 2 + 3 2 + . . &#160; &#8230; . + 1 5 n 2 is equal to

Solution

lim n → ∞ n n 2 + 1 2 + n n 2 + 2 2 + n n 2 + 3 2 + . . … . + 1 5 n 2 is equal to