How Many consecutive odd numbers will be needed to obtain sum of 10 cube. Could you please explain with formula for this question

Asked by divya.tripathy | 11th Aug, 2015, 08:33: AM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space l i s t colon 3 plus 5 equals 8 equals 2 cubed 7 plus 9 plus 11 equals 27 equals 3 cubed 13 plus 15 plus 17 plus 19 equals 64 equals 4 cubed 21 plus 23 plus 25 plus 27 plus 29 equals 125 equals 5 cubed 31 plus 33 plus 35 plus 37 plus 39 plus 41 equals 216 equals 6 cubed . . . . F o l l o w i n g space t h i s space p a t t e r n comma space i f space w e space w a n t space 10 cubed comma space t h e r e space a r e space 10 space t e r m s space i n space t h e space l i s t. T h e space f i r s t space t e r m space o f space t h e space s e r i e s space s t a r t space a s n squared minus n plus 1 equals 10 squared minus 10 plus 1 equals 100 minus 10 plus 1 equals 91 T h u s comma space t h e space e x q u a t i o n space i s 91 plus 93 plus 95 plus 97 plus 99 plus 101 plus 103 plus 105 plus 107 plus 109 equals 10 cubed S o comma space t h e r e space a r e space 10 space p o s s i b l e space c o n s e c u t i v e space o d d space n u m b e r s space s u m space u p t o space 1000.

Answered by Vimala Ramamurthy | 11th Aug, 2015, 02:19: PM