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Series

Let T n be de...

Question

Let $T_{n}$ be defined as the sum to n terms of the series T. Find $T_{34}$

$T = 2^{88} - 2^{87} - 2^{86} - 2^{85} . . . . . . .$

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Solution

The correct option is B
2⁵⁵

$T_{1} = 2^{88}$
$T_{2} = 2^{88} - 2^{87} = 2^{87} (2 - 1) = 2^{87}$
$T_{3} = 2^{88} - 2^{87} - 2^{86} = 2^{86} (2^{2} - 2^{1} - 1) = 2^{86}$
Thus, the pattern is
$T_{n} = 2^{89 - n}$
Answer is $T_{34} = 2^{55}$

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Let Tn be defined as the sum to n terms of the series T. Find T34 T=288−287−286−285.......

The correct option is B 255 T1=288 T2=288−287=287(2−1)=287 T3=288−287−286=286(22−21−1)=286 Thus, the pattern is Tn=289−n Answer is T34=255

Let $T_{n}$ be defined as the sum to n terms of the series T. Find $T_{34}$

$T = 2^{88} - 2^{87} - 2^{86} - 2^{85} . . . . . . .$

The correct option is B
2⁵⁵

$T_{1} = 2^{88}$
$T_{2} = 2^{88} - 2^{87} = 2^{87} (2 - 1) = 2^{87}$
$T_{3} = 2^{88} - 2^{87} - 2^{86} = 2^{86} (2^{2} - 2^{1} - 1) = 2^{86}$
Thus, the pattern is
$T_{n} = 2^{89 - n}$
Answer is $T_{34} = 2^{55}$