Post your math problems here #3 [And solutions to #2]

Problem: if 11987 + 21986 + 3*1985 + ... + 1986 * 2 + 1987 * 1 = 1987 * 994 * x, then what is x?

What is the sum of the infinite series 1/(2^2) + 2/(3^3) + 3/(4^4) +4/(5^5) + 5/(6^6)...? I don't know the answer at all lol

2+2=?

A block weighs half a block plus 100.
How much does a block weighs

What is the sum of the infinite series 1/(2^2) + 2/(3^3) + 3/(4^4) +4/(5^5) + 5/(6^6)...?

• It is infinite
  Sum (k-1)/k^2 = Sum (1/k - 1/k^2) = Sum (1/k) - Sum (1/k^2) = Zeta(1) - Zeta(2) = infinite - finite = infinite

@tpr said in #18:

What is the sum of the infinite series 1/(2^2) + 2/(3^3) + 3/(4^4) +4/(5^5) + 5/(6^6)...?

• It is infinite
  Sum (k-1)/k2 = Sum (1/k - 1/k2) = Sum (1/k) - Sum (1/k2) = infinite - finite = infinite
  I suppose that the sign "^" in #14 meant exponentiation. The series sum_{n=1}^{infinity} n/((n+1)^(n+1)) is convergent.

"I suppose"

• I put in 2 uppercase 2, but this site renders it as plain 2
  I edited above.
  The series is divergent.