Question

$\large{\textbf{Brain Teaser!!!}}\ [13]\\\\\textbf{\large{Title: Math Challenger}}\\\\\textbf{\large{\underline{Question:}}}\\\\\\\textsf{Is this sum finite or infinite? Justify, giving explanation or examples. }$

$\Large{\bf{\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+........}}}}}}$

$\#Be\_Brainly\\\#Together\_We\_Go\_Far$

Answer 1

Answer:

2-1n.

Step-by-step explanation:-

112+122+132+⋯+1n2

If we exclude the first rectangle, the total area of the remaining

rectangles is smaller than the area under the curvey=1x2

for1≤x≤n

Sum≤1+∫n11x2dx

=1+−1x∣∣∣n1

=1+1−1n

=2−1n.

Hope it will help you.

✨It's M.S.V.

Answer 2

Answer:

Step-by-step explanation:

112+122+132+⋯+1n2

If we exclude the first rectangle, the total area of the remaining

rectangles is smaller than the area under the curvey=1x2

for1≤x≤n

Sum≤1+∫n11x2dx

=1+−1x∣∣∣n1

=1+1−1n

=2−1n.