Question

Please show how the first few steps of this problem (IN PICTURE) are done in more detail. I do not understand how 1/(2k-1)(2k+1) = 1/2(1/(2k-1)-1/(2k+1) and then later on = n/2n+1

Conjecture a formula for the sum 1/1*3 + 1/3*5 + ... + 1/(2n-1)(2n+1), and prove your conjecture by using Mathematical Induction.

Since | 2K - | +1 ) 1QA K+) . sino (ਦਾ ' ( ਸ ) , *ਘ | - (284) ( ) : - +) = anti ' ਤ + + + - (24) : ਪੰਜ 2n +

Answer 1

--- Catercom co - A (using portal fraction) B (2K+1) one cuning partido (2k-1) (2K+1) QK) $_ TEA (2K+1) + B (2k-) put K= / TE Axo + B12x1)-1] and put k="/ LE Ax 2 +exo > A=Yq7 put all values of A and B in o (26=1)(2k) Tekst er ceken] _ * )(2+1) (2K+0) apkly Summation og = ( cekan ਵੇਚ ਕੇ both sides ਨੂੰ (2k-)(264) K1 __EŽ Hell K-1 2K+ I + I + 2+ 2X2 + 2x3- 1 2x3+1 31 | -***-***-4+4 km Anwen Ang downlod comment, please