{-1}{2}\left(\sum_{n=0}^{\infty}(-2)i^{2n}z^{2n}\right) \\
& = \sum_{n=0}^{\infty}i^{2n}z^{2n} \\
& = \sum_{n=0}^{\infty}(i^2z^2)^n \\
& = \sum_{n=0}^{\infty}(-z^2)^n
\end{aligned}\end{equation}\tag{5}\label{eq5A}$$
As you can see, this matches \eqref{eq1A}. As such, what you did was correct & I don't know why you think you weren't getting the correct result. If it was just due to the expression being different, as I show it simplifies to the same thing.

A: Your approach is all correct. Note that your sum can be rewritten as $$\frac{1}{2}\sum_{n=0}^\infty i^n ((-1)^n+1)z^n.$$
For an odd index value $n$, the term equals zero, and for even - it equals $2(-1)^kz^{2k}$, $k\in \mathbb{Z}$.
Therefore
$$\frac{1}{2}\sum_{n=0}^\infty i^n ((-1)^n+1)z^n=\frac{1}{2} ( 2-2z^2+2z^4-2z^6+\ldots)=1-z^2+z^4-z^6+\ldots$$ 
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GAME OVERI actually don't think he uses social engineering very well at all, it's certainly not his strong suite. I would say he relies very much on good old fashioned thug tactics like bribery and hard power/violence or threats of violence to remain in power and achieve his goals.

If he was actually good at social engineering he wouldn't have even needed to have this war he would have convinced the population to vote in someone friendly to him, which he has been trying to achieve for most of the last decade in various ways that have all failed miserably so this actual kinetic war is his last resort.

The only reason Putin has'support' is that those around him are basically scared of being killed and/or make a lot of money from supporting him. If that counts as social engineering then you might as well say that a guy that pulls out a gun and threatens to shoot you if you don't give him your wallet is using'social engineering' to get your money. In fact in this case Putin is the mugger who has pulled the gun, threatened to shoot you if you don't your wallet and still not got the money, so is having to actually shoot you to get what he wants. It's a massive fail IMO.Slioch was a hill I had wanted to climb for a long time. After one aborted attempt due to snow a few weeks previous, we were back in the car and making the long trek back up to Torridon. Empty roads early on a Sunday morning meant good progress and we covered the distance from Alford to Kinlochewe in under 3 hours.
The start of the standard route to Slioch starts from a large carpark in the small village of Incheril. The path meanders along the flood plain of the Kinlochewe River for a distance of 5km before it reaches the shores of Loch Maree.
The walk in is beautiful. We came across a large herd of wild Mountain Goats, grazing at the side of the loch.
Eventually, you reach a wooden bridge which crosses the Abhainn an Fhasaigh (you can see it in the picture above). Turning right immediately after the brige, the route starts the climb. Loch Maree is practically at sea level - from here it's almost 1,000 metres of ascent. Intially the route crosses moderate heathery, wet slopes past old sheilings.
After a kilometre or so, the terrain steepens and becomes rockier. The path picks a route between Sgurr Dubh and Meall Each, getting steeper until eventually we reach the corrie of Coire na Sleaghaich. We stop here for a short break, admiring the view back down to Loch Maree and the view across to the Fannichs, which are slowly beginning to reveal themselves.
The path curves left into the massive corrie. From here, we can see a zig-zag path making its way up the corrie headwall towards the twin lochans. This seems like the logical ascent route. However, there are a few walkers in front of us and they're all making for a steep grassy wall to the left of the corrie. It's nearer and it will save us crossing the peat hags in the corrie bowl so we opt to follow the crowd. I don't like steep grassy slopes. Give me something to scramble up and I'll be fine but steep grass unnerves me. Nothing for it though, but to dig in and get it over with.
Upon gaining the crest of the ridge, the views to the west opened out - Loch Maree, with Beinn Eighe towering over it, while the rest of the Torridon hills lurked in the background.
After a short rest break, we followed the wide ridge over a few undulations until the twin lochans sprang into view. The views from here were superb, lookin gup the length of Loch Maree towards Poolewe and Gairloch, with the Trotternish Peninsula of Skye and Harris in the far distance.
Another steep section next, following a badly eroded path to the right of the twin lochans. Every man for himself here- there's no single well defined route - lots of loose scree and wildlife tracks make for an abundance of possible footholds. Water was running low by this point so the patches of rapidly melting snow that were left made for a welcoming resupply. Looking back, we could see all the way to Incheril, and the start of the walk.
The air was cold in the bowl of the summit plateau and the small lochan there still had a coating of ice on it. One more short pull and we reached the trigpoint. We had a bite to eat - staked by a raven which had been following us since we climbed out of the corrie.
The views from here were magnificent in all directions. The air was crystal clear and we could see for miles - Torridon, Skye, Harris, Lewis, Gairloch, An Teallach, Fisherfield, Ben Dearg, Ben Wyvis - superb! A short walk took us over to the true summit cairn.
Originally, the plan was to retrace our steps and reverse the route back down to Loch Maree, but one look at the ridge to Sgurr an Tuill Bhain and the plan was changed. The ridge gave good walking. Initially broad, it soon narrowed down to maybe a foot in width. Some care was needed crossing the narrowest part of the ridge as it had a covering of slushy snow on it. In no time at all, we were on the summit of Sgurr an Tuill Bhan.
A short break for coffee and time for the steep descent from Sgurr an Tuill Bhain back into Coire na Sleaghaich. Real ankle-breaker stuff - deep heather and scree mix - not a place to take a header down. Soon we crossed the peat hags and rejoined the path past Meall Each, making our way back down the 2km of hillside to the banks of Loch Maree.
The walk out felt much longer than the walk in. The temperature was still high and the 5km back along the glen was a grind - past the goats, across the bridges and past the cemetery until the car park came into view at Incheril, exactly 9 hours after setting off. All that was left was a 3 hour drive back home, with pit stops at Nairn for fuel and Forres for tea.
Superb report G.Scott I still have this hill to do, so will no doubt return for reference material when it does appear on my radar. Brilliant pictures too, which will also be helpful.
You mean the stuff that