Define
A=112+152−172−1112+1132+1172−⋯,
which omits all terms of the form 1/n2 where is an odd multiple of 3, and
B=132−192+1152−1212+1272−1332+⋯,
which includes only terms of the form 1/n2 where n is an odd multiple of 3.
Determine AB.
If each sequence only had addition, this question would be much easier, but the subtraction makes it difficult for me. Help is greatly appreciated!
+26397 Define
A=112+152−172−1112+1132+1172−1192−1232+⋯,
which omits all terms of the form 1n2where is an odd multiple of 3, and
B=132−192+1152−1212+1272−1332+1392−1452+⋯,
which includes only terms of the form 1n2 where is an odd multiple of 3.
Determine AB.
A=112+152−172−1112+1132+1172−1192−1232+⋯B=132−192+1152−1212+1272−1332+1392−1452+⋯9B=112−132+152−172+192−1112+1132−1152+1172−1192+1212+⋯9B=A−132+192−1152+1212−⋯9B=A−(132−192+1152−1212+⋯⏟=B)9B=A−B10B=AAB=10
