This is an amazing identity by Abel.
Let 
![\displaystyle \sum_{k=m}^n f_k(g_{k+1}-g_k)=[f_{n+1}g_{n+1}-f_mg_m]-\sum_{k=m}^n g_{k+1}(f_{k+1}-f_k).](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+%5Csum_%7Bk%3Dm%7D%5En+f_k%28g_%7Bk%2B1%7D-g_k%29%3D%5Bf_%7Bn%2B1%7Dg_%7Bn%2B1%7D-f_mg_m%5D-%5Csum_%7Bk%3Dm%7D%5En+g_%7Bk%2B1%7D%28f_%7Bk%2B1%7D-f_k%29.&bg=ffffff&fg=333333&s=0 "\displaystyle \sum_{k=m}^n f_k(g_{k+1}-g_k)=[f_{n+1}g_{n+1}-f_mg_m]-\sum_{k=m}^n g_{k+1}(f_{k+1}-f_k).")
Advertisements
Advertisements
Advertisements
Advertisements
World News- Paul Manafort 'repeatedly and brazenly' broke law, prosecutors say in sentencing memo February 23, 2019February 24, 2019 5:03 AMNEW YORK (NYTIMES) - In a new court filing unsealed on Saturday (Feb 23), prosecutors cited sentencing guidelines that could result in a prison term of up to 22 years for Paul Manafort, President Donald Trump's former campaign chairman, for conspiracy charges to which he pleaded guilty last year.
- Paul Manafort 'repeatedly and brazenly' broke law, prosecutors say in sentencing memo February 23, 2019
- Mathematics News — ScienceDaily
- Parenthood contributes to gender imbalance in STEM employment, but it's not just an issue for mother February 18, 2019Nearly half of new moms and a quarter of new dads leave their full-time STEM jobs after they have their first child, according to a new study.
- Parenthood contributes to gender imbalance in STEM employment, but it's not just an issue for mother February 18, 2019
- Math Education
- Equity in Mathematics February 29, 2016A guest post by Beth Burroughs, Montana State UniversityYou might have noticed a recent flurry of activity by mathematicians engaged in discussions about the teaching of mathematics. A few examples:The Common Vision project is a joint effort of five organizations in the mathematical sciences (AMATYC, AMS, ASA, MAA and SIAM) focused on modernizing undergradua […]Mathematical Association of America
- Equity in Mathematics February 29, 2016
