2+4+6+...........................98+100

Asked by Kusum and Sanjeet | 15th May, 2015, 10:22: PM

Expert Answer:

2 plus 4 plus 6 plus 8 plus............. plus 100 F o r space t h e space a b o v e space s e r i e s comma t subscript 1 equals 2 t subscript 2 equals 4 t subscript 3 equals 6 t subscript 3 minus t subscript 2 equals t subscript 2 minus t subscript 1 sin c e space t h e space d i f f e r e n c e space b e t w e e n space t w o space c o n s e c u t i v e space s i d e s space i s space s a m e comma therefore space t h e space a b o v e space s e r i e s space i s space a n space A P comma T o t a l space n u m b e r space o f space t e r m s space i n space t h e space a b o v e space s e r i e s comma space n equals space 100 over 2 equals 50 L a s t space t e r m space o f space t h e space s e r i e s comma space l space equals 100 F i r s t space t e r m space o f space t h e space a b o v e space s e r i e s comma space a space equals space 2 S u m space o f space t h e space a b o v e space s e r i e s space equals space n over 2 left parenthesis a plus l right parenthesis space equals space 50 over 2 left parenthesis 2 plus 100 right parenthesis equals 25 cross times 102 over 2 equals 25 cross times 51 equals 1275

Answered by Prasenjit Paul | 16th May, 2015, 10:59: PM